[{"status":"public","type":"journal_article","publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"related_material":{"record":[{"status":"public","id":"20571","relation":"earlier_version"}]},"OA_type":"hybrid","publisher":"Springer Nature","abstract":[{"lang":"eng","text":"We prove the convergence of a modified Jordan–Kinderlehrer–Otto scheme to a solution\r\nto the Fokker–Planck equation in Ω e R^d with general—strictly positive and temporally\r\nconstant—Dirichlet boundary conditions. We work under mild assumptions on the domain,\r\nthe drift, and the initial datum. In the special case where Ω is an interval in R1, we prove\r\nthat such a solution is a gradient flow—curve of maximal slope—within a suitable space of\r\nmeasures, endowed with a modified Wasserstein distance. Our discrete scheme and modified\r\ndistance draw inspiration from contributions by A. Figalli and N. Gigli [J. Math. Pures\r\nAppl. 94, (2010), pp. 107–130], and J. Morales [J. Math. Pures Appl. 112, (2018), pp. 41–88]\r\non an optimal-transport approach to evolution equations with Dirichlet boundary conditions.\r\nSimilarly to these works, we allow the mass to flow from/to the boundary ∂Ω throughout\r\nthe evolution. However, our leading idea is to also keep track of the mass at the boundary\r\nby working with measures defined on the whole closure Ω . The driving functional is a\r\nmodification of the classical relative entropy that also makes use of the information at the\r\nboundary. As an intermediate result, when Ω is an interval in R1, we find a formula for the\r\ndescending slope of this geodesically nonconvex functional."}],"article_number":"23","scopus_import":"1","citation":{"apa":"Quattrocchi, F. (2026). Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions. <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00526-025-03193-1\">https://doi.org/10.1007/s00526-025-03193-1</a>","chicago":"Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation with General Dirichlet Boundary Conditions.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00526-025-03193-1\">https://doi.org/10.1007/s00526-025-03193-1</a>.","mla":"Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation with General Dirichlet Boundary Conditions.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 65, no. 1, 23, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s00526-025-03193-1\">10.1007/s00526-025-03193-1</a>.","ista":"Quattrocchi F. 2026. Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions. Calculus of Variations and Partial Differential Equations. 65(1), 23.","short":"F. Quattrocchi, Calculus of Variations and Partial Differential Equations 65 (2026).","ieee":"F. Quattrocchi, “Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 65, no. 1. Springer Nature, 2026.","ama":"Quattrocchi F. Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions. <i>Calculus of Variations and Partial Differential Equations</i>. 2026;65(1). doi:<a href=\"https://doi.org/10.1007/s00526-025-03193-1\">10.1007/s00526-025-03193-1</a>"},"oa_version":"Published Version","month":"01","date_updated":"2026-04-07T08:37:46Z","quality_controlled":"1","external_id":{"arxiv":["2403.07803"]},"arxiv":1,"date_published":"2026-01-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","acknowledgement":"The author would like to thank Jan Maas for suggesting this project and for many helpful comments, Antonio Agresti, Lorenzo Dello Schiavo and Julian Fischer for several fruitful discussions, Oliver Tse for pointing out the reference [10], and the anonymous reviewer for carefully reading this manuscript and providing valuable suggestions. He also gratefully acknowledges support from the Austrian Science Fund (FWF) project 10.55776/F65.Open access funding provided by Institute of Science and Technology (IST Austria).","title":"Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions","PlanS_conform":"1","volume":65,"publication":"Calculus of Variations and Partial Differential Equations","OA_place":"publisher","corr_author":"1","day":"01","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","_id":"20865","department":[{"_id":"JaMa"}],"issue":"1","intvolume":"        65","oa":1,"publication_status":"published","doi":"10.1007/s00526-025-03193-1","file":[{"content_type":"application/pdf","date_updated":"2026-01-05T12:36:39Z","relation":"main_file","file_size":958382,"file_id":"20945","success":1,"date_created":"2026-01-05T12:36:39Z","access_level":"open_access","file_name":"2026_CalculusVariations_Quattrocchi.pdf","creator":"dernst","checksum":"635370d64abaf444f50f5cca60bba1be"}],"project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"ddc":["510"],"language":[{"iso":"eng"}],"author":[{"id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308","full_name":"Quattrocchi, Filippo","first_name":"Filippo","last_name":"Quattrocchi","orcid":"0009-0000-9773-1931"}],"file_date_updated":"2026-01-05T12:36:39Z","article_type":"original","date_created":"2025-12-29T12:06:26Z","year":"2026"},{"PlanS_conform":"1","title":"Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation","date_published":"2026-01-01T00:00:00Z","arxiv":1,"article_processing_charge":"Yes (in subscription journal)","acknowledgement":"All authors gratefully acknowledge funding from the Austrian Science Fund (FWF) through the project F65. CR gratefully acknowledges support from the Austrian Science Fund (FWF), grants P30000, P33010, W1245. FC gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411.","volume":54,"month":"01","external_id":{"arxiv":["2303.00429"]},"quality_controlled":"1","date_updated":"2026-05-21T07:21:25Z","publisher":"Institute of Mathematical Statistics","citation":{"ieee":"F. Cornalba, J. L. Fischer, J. Ingmanns, and C. Raithel, “Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation,” <i>The Annals of Probability</i>, vol. 54, no. 1. Institute of Mathematical Statistics, pp. 155–215, 2026.","ama":"Cornalba F, Fischer JL, Ingmanns J, Raithel C. Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation. <i>The Annals of Probability</i>. 2026;54(1):155-215. doi:<a href=\"https://doi.org/10.1214/25-aop1763\">10.1214/25-aop1763</a>","chicago":"Cornalba, Federico, Julian L Fischer, Jonas Ingmanns, and Claudia Raithel. “Density Fluctuations in Weakly Interacting Particle Systems via the Dean–Kawasaki Equation.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2026. <a href=\"https://doi.org/10.1214/25-aop1763\">https://doi.org/10.1214/25-aop1763</a>.","apa":"Cornalba, F., Fischer, J. L., Ingmanns, J., &#38; Raithel, C. (2026). Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/25-aop1763\">https://doi.org/10.1214/25-aop1763</a>","ista":"Cornalba F, Fischer JL, Ingmanns J, Raithel C. 2026. Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation. The Annals of Probability. 54(1), 155–215.","short":"F. Cornalba, J.L. Fischer, J. Ingmanns, C. Raithel, The Annals of Probability 54 (2026) 155–215.","mla":"Cornalba, Federico, et al. “Density Fluctuations in Weakly Interacting Particle Systems via the Dean–Kawasaki Equation.” <i>The Annals of Probability</i>, vol. 54, no. 1, Institute of Mathematical Statistics, 2026, pp. 155–215, doi:<a href=\"https://doi.org/10.1214/25-aop1763\">10.1214/25-aop1763</a>."},"keyword":["Weakly interacting particle systems","fluctuating hydrodynamics","Dean-Kawasaki equation","stochastic PDEs","numerical approximation"],"scopus_import":"1","abstract":[{"lang":"eng","text":"The Dean–Kawasaki equation—one of the most fundamental SPDEs of\r\nfluctuating hydrodynamics—has been proposed as a model for density fluctuations in weakly interacting particle systems. In its original form, it is highly\r\nsingular and fails to be renormalizable, even by approaches such as regularity structures and paracontrolled distributions, hindering mathematical approaches to its rigorous justification. It has been understood recently that it is\r\nnatural to introduce a suitable regularization, for example, by applying a formal spatial discretization or by truncating high-frequency noise: This yields\r\nwell-posed equations that should still precisely approximate the law of the\r\nparticle density fluctuations.\r\nIn the present work, we prove that a regularization in the form of a formal\r\ndiscretization of the Dean–Kawasaki equation indeed accurately describes\r\ndensity fluctuations in systems of weakly interacting diffusing particles: We\r\nshow that, in suitable weak metrics, the law of fluctuations as predicted by\r\nthe discretized Dean–Kawasaki SPDE approximates the law of fluctuations\r\nof the original particle system, up to an error that is of arbitrarily high order in\r\nthe inverse particle number and a discretization error. In particular, the Dean–\r\nKawasaki equation provides a means for efficient and accurate simulations of\r\ndensity fluctuations in weakly interacting particle systems."}],"oa_version":"Published Version","type":"journal_article","publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"status":"public","OA_type":"hybrid","date_created":"2026-05-20T08:25:25Z","article_type":"original","year":"2026","publication_status":"published","oa":1,"doi":"10.1214/25-aop1763","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"file":[{"date_updated":"2026-05-21T07:11:27Z","relation":"main_file","content_type":"application/pdf","file_size":865745,"success":1,"file_id":"21906","date_created":"2026-05-21T07:11:27Z","file_name":"2026_AnnalsProbability_Cornalba.pdf","access_level":"open_access","checksum":"3e60c0e25a1c96342029a7d2b031505f","creator":"dernst"}],"intvolume":"        54","APC_amount":"1352,08 EUR","file_date_updated":"2026-05-21T07:11:27Z","ddc":["510"],"language":[{"iso":"eng"}],"author":[{"first_name":"Federico","last_name":"Cornalba","full_name":"Cornalba, Federico"},{"full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X","first_name":"Julian L","last_name":"Fischer"},{"first_name":"Jonas","last_name":"Ingmanns","orcid":"0009-0008-1310-7946","id":"71523d30-15b2-11ec-abd3-f80aa909d6b0","full_name":"Ingmanns, Jonas"},{"full_name":"Raithel, Claudia","first_name":"Claudia","last_name":"Raithel"}],"page":"155-215","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"21894","issue":"1","department":[{"_id":"JuFi"}],"ec_funded":1,"OA_place":"publisher","corr_author":"1","publication":"The Annals of Probability","day":"01"},{"publisher":"Institute of Science and Technology Austria","oa_version":"Published Version","citation":{"ista":"Khudiakova K. 2026. How epistasis and purifying selection shape genetic diversity. Institute of Science and Technology Austria.","short":"K. Khudiakova, How Epistasis and Purifying Selection Shape Genetic Diversity, Institute of Science and Technology Austria, 2026.","mla":"Khudiakova, Kseniia. <i>How Epistasis and Purifying Selection Shape Genetic Diversity</i>. Institute of Science and Technology Austria, 2026, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-21918\">10.15479/AT-ISTA-21918</a>.","chicago":"Khudiakova, Kseniia. “How Epistasis and Purifying Selection Shape Genetic Diversity.” Institute of Science and Technology Austria, 2026. <a href=\"https://doi.org/10.15479/AT-ISTA-21918\">https://doi.org/10.15479/AT-ISTA-21918</a>.","apa":"Khudiakova, K. (2026). <i>How epistasis and purifying selection shape genetic diversity</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-21918\">https://doi.org/10.15479/AT-ISTA-21918</a>","ama":"Khudiakova K. How epistasis and purifying selection shape genetic diversity. 2026. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-21918\">10.15479/AT-ISTA-21918</a>","ieee":"K. Khudiakova, “How epistasis and purifying selection shape genetic diversity,” Institute of Science and Technology Austria, 2026."},"publication_identifier":{"issn":["2663-337X"]},"type":"dissertation","status":"public","related_material":{"record":[{"relation":"part_of_dissertation","id":"11447","status":"public"},{"status":"deleted","id":"12513","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"21967","status":"public"},{"id":"21968","relation":"part_of_dissertation","status":"public"}]},"title":"How epistasis and purifying selection shape genetic diversity","acknowledgement":"At different stages of my PhD, my work was supported by several grants: the\r\nDOC fellowship of the Austrian Academy of Sciences (26293, awarded to me),\r\nthe FWF-SFB grant (PT1032F06504 n. F65, awarded to Jan Maas), and the ERC\r\ngrant (PR1032ERC01 n. 716117, awarded to Jan Maas). I also appreciate the help\r\nfrom the Scientific Computing unit for their advice on the cluster usage.","date_published":"2026-06-07T00:00:00Z","article_processing_charge":"No","acknowledged_ssus":[{"_id":"ScienComp"}],"month":"06","date_updated":"2026-06-12T12:43:35Z","page":"89","has_accepted_license":"1","supervisor":[{"first_name":"Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","full_name":"Barton, Nicholas H"},{"first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan"}],"tmp":{"short":"CC BY-NC-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"department":[{"_id":"GradSch"},{"_id":"NiBa"},{"_id":"JaMa"}],"ec_funded":1,"_id":"21918","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","corr_author":"1","OA_place":"publisher","day":"07","date_created":"2026-05-27T06:26:08Z","alternative_title":["ISTA Thesis"],"year":"2026","doi":"10.15479/AT-ISTA-21918","project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"},{"_id":"34d33d68-11ca-11ed-8bc3-ec13763c0ca8","grant_number":"26293","name":"The impact of deleterious mutations on small populations"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"file":[{"file_id":"21965","date_created":"2026-06-09T08:34:38Z","file_name":"thesis.zip","access_level":"closed","checksum":"0cff64ae74f0f9f2d7011700c82f700a","creator":"kkhudiak","date_updated":"2026-06-09T08:40:48Z","content_type":"application/x-zip-compressed","relation":"source_file","file_size":20549813},{"file_id":"21969","date_created":"2026-06-09T12:28:51Z","embargo_to":"open_access","file_name":"2026_Khudiakova_Ksenia_Thesis.pdf","access_level":"closed","creator":"kkhudiak","checksum":"547ae42de37cc86894af283f1664dbc8","relation":"main_file","content_type":"application/pdf","date_updated":"2026-06-11T12:14:53Z","file_size":9387029,"embargo":"2027-06-10"}],"publication_status":"published","degree_awarded":"PhD","file_date_updated":"2026-06-11T12:14:53Z","author":[{"orcid":"0000-0002-6246-1465","last_name":"Khudiakova","first_name":"Kseniia","full_name":"Khudiakova, Kseniia","id":"4E6DC800-AE37-11E9-AC72-31CAE5697425"}],"language":[{"iso":"eng"}],"ddc":["576"]},{"has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"department":[{"_id":"JaMa"}],"issue":"1","ec_funded":1,"_id":"20814","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_place":"publisher","publication":"Potential Analysis","researchdata_availability":"no","day":"01","date_created":"2025-12-14T23:02:03Z","article_type":"original","year":"2026","doi":"10.1007/s11118-025-10251-y","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups"}],"file":[{"content_type":"application/pdf","relation":"main_file","date_updated":"2026-07-27T10:25:21Z","file_size":445935,"access_level":"open_access","file_name":"2026_PotentialAnalysis_Keller.pdf","creator":"dernst","checksum":"9f5a4e900b8d4c74c6b5bf7c3bad54e1","file_id":"22414","success":1,"date_created":"2026-07-27T10:25:21Z"}],"publication_status":"published","oa":1,"mathsc":["31C15","31C25","35A15","35J10","47D07"],"intvolume":"        64","dataavailabilitystatement":"No datasets were generated or analysed during the current study.","file_date_updated":"2026-07-27T10:25:21Z","author":[{"first_name":"Matthias","last_name":"Keller","full_name":"Keller, Matthias"},{"first_name":"Daniel","last_name":"Lenz","full_name":"Lenz, Daniel"},{"first_name":"Marcel","last_name":"Schmidt","full_name":"Schmidt, Marcel"},{"last_name":"Schwarz","first_name":"Michael","full_name":"Schwarz, Michael"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior","first_name":"Melchior","last_name":"Wirth","orcid":"0000-0002-0519-4241"}],"language":[{"iso":"eng"}],"ddc":["510"],"publisher":"Springer Nature","das_tickbox":"1","oa_version":"Published Version","abstract":[{"text":"We characterize all semigroups sandwiched between the semigroup of a Dirichlet form and the semigroup of its active main part. In case the Dirichlet form is regular, we give a more explicit description of the quadratic forms of the sandwiched semigroups in terms of pairs consisting of an open set and a measure on an abstract boundary.","lang":"eng"}],"citation":{"ama":"Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. <i>Potential Analysis</i>. 2026;64(1). doi:<a href=\"https://doi.org/10.1007/s11118-025-10251-y\">10.1007/s11118-025-10251-y</a>","ieee":"M. Keller, D. Lenz, M. Schmidt, M. Schwarz, and M. Wirth, “Boundary representations of intermediate forms between a regular Dirichlet form and its active main part,” <i>Potential Analysis</i>, vol. 64, no. 1. Springer Nature, 2026.","short":"M. Keller, D. Lenz, M. Schmidt, M. Schwarz, M. Wirth, Potential Analysis 64 (2026).","ista":"Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. 2026. Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. Potential Analysis. 64(1), 6.","mla":"Keller, Matthias, et al. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>, vol. 64, no. 1, 6, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s11118-025-10251-y\">10.1007/s11118-025-10251-y</a>.","chicago":"Keller, Matthias, Daniel Lenz, Marcel Schmidt, Michael Schwarz, and Melchior Wirth. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s11118-025-10251-y\">https://doi.org/10.1007/s11118-025-10251-y</a>.","apa":"Keller, M., Lenz, D., Schmidt, M., Schwarz, M., &#38; Wirth, M. (2026). Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-025-10251-y\">https://doi.org/10.1007/s11118-025-10251-y</a>"},"scopus_import":"1","article_number":"6","keyword":["Dirichlet forms","Domination of semigroups","Dirichlet","Neumann and Robin boundary conditions"],"publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"type":"journal_article","status":"public","supplementarymaterial":"no","OA_type":"hybrid","PlanS_conform":"1","title":"Boundary representations of intermediate forms between a regular Dirichlet form and its active main part","acknowledgement":"Open Access funding enabled and organized by Projekt DEAL. The first three authors acknowledge financial support of the DFG within the priority programme Geometry at Infinity.\r\nM.W. acknowledges financial support by the German Academic Scholarship Foundation, by the Austrian Science Fund (FWF) through grant number F65 and the Esprit Programme [ESP 156], and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117).","date_published":"2026-01-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","arxiv":1,"volume":64,"month":"01","external_id":{"arxiv":["2301.01035"]},"quality_controlled":"1","date_updated":"2026-07-27T10:25:46Z"},{"author":[{"first_name":"Lorenzo","last_name":"Portinale","full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0009-0000-9773-1931","last_name":"Quattrocchi","first_name":"Filippo","full_name":"Quattrocchi, Filippo","id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308"}],"ddc":["500"],"language":[{"iso":"eng"}],"file_date_updated":"2026-07-23T05:55:03Z","intvolume":"        37","file":[{"content_type":"application/pdf","date_updated":"2026-07-23T05:55:03Z","relation":"main_file","file_size":612317,"file_id":"22386","success":1,"date_created":"2026-07-23T05:55:03Z","access_level":"open_access","file_name":"2026_EuropJourAppliedMath_Portinale.pdf","checksum":"d038f4d00cbfbde2672c17138eab21c9","creator":"dernst"}],"project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"doi":"10.1017/s0956792524000810","publication_status":"published","oa":1,"DOAJ_listed":"1","year":"2026","article_type":"original","date_created":"2024-12-23T11:03:59Z","researchdata_availability":"no","day":"01","publication":"European Journal of Applied Mathematics","OA_place":"publisher","issue":"3","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"_id":"18706","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"page":"614-642","date_updated":"2026-08-07T22:31:04Z","quality_controlled":"1","external_id":{"isi":["001381435800001"]},"month":"06","volume":37,"isi":1,"acknowledgement":"L.P. gratefully acknowledges fundings from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – GZ 2047/1, Projekt-ID 390685813. F.Q. gratefully acknowledges support from the Austrian Science Fund (FWF) project 10.55776/F65.","article_processing_charge":"Yes","date_published":"2026-06-01T00:00:00Z","PlanS_conform":"1","title":"Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs","OA_type":"gold","related_material":{"record":[{"relation":"dissertation_contains","id":"20563","status":"public"}]},"supplementarymaterial":"no","status":"public","publication_identifier":{"issn":["0956-7925"],"eissn":["1469-4425"]},"type":"journal_article","oa_version":"Published Version","keyword":["optimal transport","discrete-to-continuum","homogenisation","linear growth","gamma-convergence"],"citation":{"ama":"Portinale L, Quattrocchi F. Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs. <i>European Journal of Applied Mathematics</i>. 2026;37(3):614-642. doi:<a href=\"https://doi.org/10.1017/s0956792524000810\">10.1017/s0956792524000810</a>","ieee":"L. Portinale and F. Quattrocchi, “Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs,” <i>European Journal of Applied Mathematics</i>, vol. 37, no. 3. Cambridge University Press, pp. 614–642, 2026.","short":"L. Portinale, F. Quattrocchi, European Journal of Applied Mathematics 37 (2026) 614–642.","ista":"Portinale L, Quattrocchi F. 2026. Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs. European Journal of Applied Mathematics. 37(3), 614–642.","mla":"Portinale, Lorenzo, and Filippo Quattrocchi. “Discrete-to-Continuum Limits of Optimal Transport with Linear Growth on Periodic Graphs.” <i>European Journal of Applied Mathematics</i>, vol. 37, no. 3, Cambridge University Press, 2026, pp. 614–42, doi:<a href=\"https://doi.org/10.1017/s0956792524000810\">10.1017/s0956792524000810</a>.","chicago":"Portinale, Lorenzo, and Filippo Quattrocchi. “Discrete-to-Continuum Limits of Optimal Transport with Linear Growth on Periodic Graphs.” <i>European Journal of Applied Mathematics</i>. Cambridge University Press, 2026. <a href=\"https://doi.org/10.1017/s0956792524000810\">https://doi.org/10.1017/s0956792524000810</a>.","apa":"Portinale, L., &#38; Quattrocchi, F. (2026). Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs. <i>European Journal of Applied Mathematics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s0956792524000810\">https://doi.org/10.1017/s0956792524000810</a>"},"scopus_import":"1","abstract":[{"text":"We prove discrete-to-continuum convergence for dynamical optimal transport on  Zd\r\n -periodic graphs with cost functional having linear growth at infinity. This result provides an answer to a problem left open by Gladbach, Kopfer, Maas, and Portinale (Calc Var Partial Differential Equations 62(5), 2023), where the convergence behaviour of discrete boundary-value dynamical transport problems is proved under the stronger assumption of superlinear growth. Our result extends the known literature to some important classes of examples, such as scaling limits of  1 -Wasserstein transport problems. Similarly to what happens in the quadratic case, the geometry of the graph plays a crucial role in the structure of the limit cost function, as we discuss in the final part of this work, which includes some visual representations.","lang":"eng"}],"das_tickbox":"0","publisher":"Cambridge University Press"},{"date_created":"2024-12-08T23:01:56Z","article_type":"original","year":"2025","publication_status":"published","oa":1,"project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"}],"doi":"10.1002/mana.202400169","file":[{"file_size":1734511,"date_updated":"2025-01-13T10:34:42Z","relation":"main_file","content_type":"application/pdf","date_created":"2025-01-13T10:34:42Z","file_id":"18838","success":1,"creator":"dernst","checksum":"1dc50d156feb777c86d779fb1c9ac875","access_level":"open_access","file_name":"2025_MathNachrichten_DelloSchiavo.pdf"}],"intvolume":"       298","file_date_updated":"2025-01-13T10:34:42Z","ddc":["510"],"language":[{"iso":"eng"}],"author":[{"orcid":"0000-0002-9881-6870","first_name":"Lorenzo","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"first_name":"Ronan","last_name":"Herry","full_name":"Herry, Ronan"},{"full_name":"Kopfer, Eva","first_name":"Eva","last_name":"Kopfer"},{"last_name":"Sturm","first_name":"Karl Theodor","full_name":"Sturm, Karl Theodor"}],"page":"244-281","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"18632","ec_funded":1,"department":[{"_id":"JaMa"}],"issue":"1","OA_place":"publisher","publication":"Mathematische Nachrichten","day":"01","title":"Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous","arxiv":1,"article_processing_charge":"Yes (via OA deal)","date_published":"2025-01-01T00:00:00Z","isi":1,"acknowledgement":"KTS is grateful to Christoph Thiele for valuable discussions and helpful references. LDS is grateful to Nathanaël Berestycki for valuable discussions on Gaussian Multiplicative Chaoses. The authors are grateful to an anonymous reviewer for suggestions which improved the presentation.\r\nThe authors gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft through the project ‘Random Riemannian Geometry’ within the SPP 2265 ‘Random Geometric Systems.'\r\nLDS gratefully acknowledges financial support from the European Research Council (grant agreement No. 716117, awarded to J. Maas) and from the Austrian Science Fund (FWF). His research was funded by the Austrian Science Fund (FWF) project 10.55776/F65 and project 10.55776/ESP208.\r\nRH, EK, and KTS gratefully acknowledge funding by the Hausdorff Center for Mathematics (project ID 390685813), and through project B03 within the CRC 1060 (project ID 211504053). RH and KTS also gratefully acknowledges financial support from the European Research Council through the ERC AdG ‘RicciBounds’ (grant agreement 694405).\r\nOpen access funding enabled and organized by Projekt DEAL.","volume":298,"month":"01","external_id":{"isi":["001366948500001"],"arxiv":["2302.02963"]},"quality_controlled":"1","date_updated":"2025-04-14T07:27:49Z","publisher":"Wiley","scopus_import":"1","citation":{"ama":"Dello Schiavo L, Herry R, Kopfer E, Sturm KT. Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous. <i>Mathematische Nachrichten</i>. 2025;298(1):244-281. doi:<a href=\"https://doi.org/10.1002/mana.202400169\">10.1002/mana.202400169</a>","ieee":"L. Dello Schiavo, R. Herry, E. Kopfer, and K. T. Sturm, “Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous,” <i>Mathematische Nachrichten</i>, vol. 298, no. 1. Wiley, pp. 244–281, 2025.","ista":"Dello Schiavo L, Herry R, Kopfer E, Sturm KT. 2025. Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous. Mathematische Nachrichten. 298(1), 244–281.","short":"L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Mathematische Nachrichten 298 (2025) 244–281.","mla":"Dello Schiavo, Lorenzo, et al. “Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary Dimension: From Discrete to Continuous.” <i>Mathematische Nachrichten</i>, vol. 298, no. 1, Wiley, 2025, pp. 244–81, doi:<a href=\"https://doi.org/10.1002/mana.202400169\">10.1002/mana.202400169</a>.","chicago":"Dello Schiavo, Lorenzo, Ronan Herry, Eva Kopfer, and Karl Theodor Sturm. “Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary Dimension: From Discrete to Continuous.” <i>Mathematische Nachrichten</i>. Wiley, 2025. <a href=\"https://doi.org/10.1002/mana.202400169\">https://doi.org/10.1002/mana.202400169</a>.","apa":"Dello Schiavo, L., Herry, R., Kopfer, E., &#38; Sturm, K. T. (2025). Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous. <i>Mathematische Nachrichten</i>. Wiley. <a href=\"https://doi.org/10.1002/mana.202400169\">https://doi.org/10.1002/mana.202400169</a>"},"abstract":[{"text":"For an arbitrary dimension (Formula presented.), we study: the polyharmonic Gaussian field (Formula presented.) on the discrete torus (Formula presented.), that is the random field whose law on (Formula presented.) given by (Formula presented.) where (Formula presented.) is the Lebesgue measure and (Formula presented.) is the discrete Laplacian; the associated discrete Liouville quantum gravity (LQG) measure associated with it, that is, the random measure on (Formula presented.) (Formula presented.) where (Formula presented.) is a regularity parameter. As (Formula presented.), we prove convergence of the fields (Formula presented.) to the polyharmonic Gaussian field (Formula presented.) on the continuous torus (Formula presented.), as well as convergence of the random measures (Formula presented.) to the LQG measure (Formula presented.) on (Formula presented.), for all (Formula presented.). ","lang":"eng"}],"oa_version":"Published Version","type":"journal_article","publication_identifier":{"issn":["0025-584X"],"eissn":["1522-2616"]},"status":"public","OA_type":"hybrid"},{"has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"page":"262-287","department":[{"_id":"JuFi"}],"issue":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"19027","publication":"SIAM Journal on Numerical Analysis","corr_author":"1","OA_place":"publisher","day":"01","article_type":"original","date_created":"2025-02-16T23:02:34Z","year":"2025","intvolume":"        63","file":[{"content_type":"application/pdf","relation":"main_file","date_updated":"2025-02-17T08:32:23Z","file_size":2435019,"success":1,"file_id":"19029","date_created":"2025-02-17T08:32:23Z","file_name":"2025_SIAMNumerAnaly_Cornalba.pdf","access_level":"open_access","checksum":"53505647e848ed50f7e0d00c369b14e7","creator":"dernst"}],"doi":"10.1137/23M1617345","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"oa":1,"publication_status":"published","author":[{"id":"2CEB641C-A400-11E9-A717-D712E6697425","full_name":"Cornalba, Federico","first_name":"Federico","last_name":"Cornalba","orcid":"0000-0002-6269-5149"},{"orcid":"0000-0002-0479-558X","first_name":"Julian L","last_name":"Fischer","full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"}],"language":[{"iso":"eng"}],"ddc":["510"],"file_date_updated":"2025-02-17T08:32:23Z","publisher":"Society for Industrial and Applied Mathematics","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Stochastic PDEs of fluctuating hydrodynamics are a powerful tool for the description of fluctuations in many-particle systems. In this paper, we develop and analyze a multilevel Monte Carlo (MLMC) scheme for the Dean–Kawasaki equation, a pivotal representative of this class of SPDEs. We prove analytically and demonstrate numerically that our MLMC scheme provides a significant reduction in computational cost (with respect to a standard Monte Carlo method) in the simulation of the Dean–Kawasaki equation. Specifically, we link this reduction in cost to having a sufficiently large average particle density and show that sizeable cost reductions can be obtained even when we have solutions with regions of low density. Numerical simulations are provided in the two-dimensional case, confirming our theoretical predictions. Our results are formulated entirely in terms of the law of distributions rather than in terms of strong spatial norms: this crucially allows for MLMC speed-ups altogether despite the Dean–Kawasaki equation being highly singular."}],"scopus_import":"1","citation":{"apa":"Cornalba, F., &#38; Fischer, J. L. (2025). Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating hydrodynamics. <i>SIAM Journal on Numerical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/23M1617345\">https://doi.org/10.1137/23M1617345</a>","chicago":"Cornalba, Federico, and Julian L Fischer. “Multilevel Monte Carlo Methods for the Dean–Kawasaki Equation from Fluctuating Hydrodynamics.” <i>SIAM Journal on Numerical Analysis</i>. Society for Industrial and Applied Mathematics, 2025. <a href=\"https://doi.org/10.1137/23M1617345\">https://doi.org/10.1137/23M1617345</a>.","mla":"Cornalba, Federico, and Julian L. Fischer. “Multilevel Monte Carlo Methods for the Dean–Kawasaki Equation from Fluctuating Hydrodynamics.” <i>SIAM Journal on Numerical Analysis</i>, vol. 63, no. 1, Society for Industrial and Applied Mathematics, 2025, pp. 262–87, doi:<a href=\"https://doi.org/10.1137/23M1617345\">10.1137/23M1617345</a>.","short":"F. Cornalba, J.L. Fischer, SIAM Journal on Numerical Analysis 63 (2025) 262–287.","ista":"Cornalba F, Fischer JL. 2025. Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating hydrodynamics. SIAM Journal on Numerical Analysis. 63(1), 262–287.","ieee":"F. Cornalba and J. L. Fischer, “Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating hydrodynamics,” <i>SIAM Journal on Numerical Analysis</i>, vol. 63, no. 1. Society for Industrial and Applied Mathematics, pp. 262–287, 2025.","ama":"Cornalba F, Fischer JL. Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating hydrodynamics. <i>SIAM Journal on Numerical Analysis</i>. 2025;63(1):262-287. doi:<a href=\"https://doi.org/10.1137/23M1617345\">10.1137/23M1617345</a>"},"status":"public","publication_identifier":{"issn":["0036-1429"],"eissn":["1095-7170"]},"type":"journal_article","OA_type":"hybrid","isi":1,"acknowledgement":"The work of the authors was supported by the Austrian Science Fund (FWF) projectF65.","article_processing_charge":"Yes (in subscription journal)","date_published":"2025-02-01T00:00:00Z","arxiv":1,"title":"Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating hydrodynamics","volume":63,"month":"02","date_updated":"2025-09-30T10:30:31Z","quality_controlled":"1","external_id":{"arxiv":["2311.08872"],"isi":["001447583400011"]}},{"publication":"The Annals of Applied Probability","OA_place":"repository","corr_author":"1","day":"01","page":"196 - 250","ec_funded":1,"department":[{"_id":"JaMa"}],"issue":"1","_id":"20040","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        35","doi":"10.1214/24-aap2113","project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"oa":1,"publication_status":"published","author":[{"first_name":"Francesco","last_name":"Pedrotti","full_name":"Pedrotti, Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"}],"language":[{"iso":"eng"}],"article_type":"original","date_created":"2025-07-21T07:49:15Z","year":"2025","status":"public","publication_identifier":{"issn":["1050-5164"]},"type":"journal_article","related_material":{"record":[{"id":"17351","relation":"earlier_version","status":"public"}]},"OA_type":"green","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2308.00516","open_access":"1"}],"publisher":"Institute of Mathematical Statistics","oa_version":"Preprint","abstract":[{"lang":"eng","text":"Contractive coupling rates have been recently introduced by Conforti as a tool to establish convex Sobolev inequalities (including modified log-Sobolev and Poincaré inequality) for some classes of Markov chains. In this work, for most of the examples discussed by Conforti, we use contractive coupling rates to prove stronger inequalities, in the form of curvature lower bounds (in entropic and discrete Bakry–Émery sense) and geodesic convexity of some entropic functionals. In addition, we recall and give straightforward generalizations of some notions of coarse Ricci curvature, and we discuss some of their properties and relations with the concepts of couplings and coupling rates: as an application, we show exponential contraction of the p-Wasserstein distance for the heat flow in the aforementioned examples."}],"citation":{"ama":"Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. <i>The Annals of Applied Probability</i>. 2025;35(1):196-250. doi:<a href=\"https://doi.org/10.1214/24-aap2113\">10.1214/24-aap2113</a>","ieee":"F. Pedrotti, “Contractive coupling rates and curvature lower bounds for Markov chains,” <i>The Annals of Applied Probability</i>, vol. 35, no. 1. Institute of Mathematical Statistics, pp. 196–250, 2025.","mla":"Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” <i>The Annals of Applied Probability</i>, vol. 35, no. 1, Institute of Mathematical Statistics, 2025, pp. 196–250, doi:<a href=\"https://doi.org/10.1214/24-aap2113\">10.1214/24-aap2113</a>.","short":"F. Pedrotti, The Annals of Applied Probability 35 (2025) 196–250.","ista":"Pedrotti F. 2025. Contractive coupling rates and curvature lower bounds for Markov chains. The Annals of Applied Probability. 35(1), 196–250.","apa":"Pedrotti, F. (2025). Contractive coupling rates and curvature lower bounds for Markov chains. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/24-aap2113\">https://doi.org/10.1214/24-aap2113</a>","chicago":"Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/24-aap2113\">https://doi.org/10.1214/24-aap2113</a>."},"scopus_import":"1","month":"02","date_updated":"2025-11-05T13:50:07Z","quality_controlled":"1","external_id":{"isi":["001434322900006"],"arxiv":["2308.00516"]},"acknowledgement":"The author warmly thanks Jan Maas for suggesting the project and for his guidance, and Melchior Wirth and Haonan Zhang for useful discussions. The author is also grateful to an anonymous reviewer for carefully reading the manuscript and providing many valuable suggestions. The author gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme\r\n(grant agreement No. 716117) and by the Austrian Science Fund (FWF), Project SFB F65.","isi":1,"arxiv":1,"date_published":"2025-02-01T00:00:00Z","article_processing_charge":"No","title":"Contractive coupling rates and curvature lower bounds for Markov chains","volume":35},{"language":[{"iso":"eng"}],"author":[{"last_name":"Khudiakova","first_name":"Kseniia","orcid":"0000-0002-6246-1465","id":"4E6DC800-AE37-11E9-AC72-31CAE5697425","full_name":"Khudiakova, Kseniia"},{"last_name":"Maas","first_name":"Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan"},{"last_name":"Pedrotti","first_name":"Francesco","full_name":"Pedrotti, Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"}],"intvolume":"        35","oa":1,"publication_status":"published","doi":"10.1214/25-aap2162","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"name":"The impact of deleterious mutations on small populations","grant_number":"26293","_id":"34d33d68-11ca-11ed-8bc3-ec13763c0ca8"}],"year":"2025","article_type":"original","date_created":"2025-07-21T08:13:54Z","day":"01","publication":"The Annals of Applied Probability","corr_author":"1","OA_place":"repository","_id":"20050","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","department":[{"_id":"JaMa"}],"issue":"3","page":"1913-1940","quality_controlled":"1","date_updated":"2025-09-30T14:12:48Z","external_id":{"arxiv":["2402.04151"],"isi":["001523520000012"]},"month":"06","volume":35,"article_processing_charge":"No","arxiv":1,"date_published":"2025-06-01T00:00:00Z","isi":1,"acknowledgement":"This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/F65 and the Austrian Academy of Science, DOC fellowship nr. 26293.","title":"L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model","OA_type":"green","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"17352"}]},"status":"public","type":"journal_article","publication_identifier":{"issn":["1050-5164"]},"scopus_import":"1","abstract":[{"text":"We prove upper bounds on the L∞-Wasserstein distance from optimal transport between strongly log-concave probability densities and log-Lipschitz perturbations. In the simplest setting, such a bound amounts to a transport-information inequality involving the L∞-Wasserstein metric and the relative L∞-Fisher information. We show that this inequality can be sharpened significantly in situations where the involved densities are anisotropic. Our proof is based on probabilistic techniques using Langevin dynamics. As an application of these results, we obtain sharp exponential rates of convergence in Fisher’s infinitesimal model from quantitative genetics, generalising recent results by Calvez, Poyato, and Santambrogio in dimension 1 to arbitrary dimensions.","lang":"eng"}],"citation":{"ieee":"K. Khudiakova, J. Maas, and F. Pedrotti, “L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model,” <i>The Annals of Applied Probability</i>, vol. 35, no. 3. Institute of Mathematical Statistics, pp. 1913–1940, 2025.","ama":"Khudiakova K, Maas J, Pedrotti F. L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. <i>The Annals of Applied Probability</i>. 2025;35(3):1913-1940. doi:<a href=\"https://doi.org/10.1214/25-aap2162\">10.1214/25-aap2162</a>","apa":"Khudiakova, K., Maas, J., &#38; Pedrotti, F. (2025). L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/25-aap2162\">https://doi.org/10.1214/25-aap2162</a>","chicago":"Khudiakova, Kseniia, Jan Maas, and Francesco Pedrotti. “L∞-Optimal Transport of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/25-aap2162\">https://doi.org/10.1214/25-aap2162</a>.","mla":"Khudiakova, Kseniia, et al. “L∞-Optimal Transport of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” <i>The Annals of Applied Probability</i>, vol. 35, no. 3, Institute of Mathematical Statistics, 2025, pp. 1913–40, doi:<a href=\"https://doi.org/10.1214/25-aap2162\">10.1214/25-aap2162</a>.","short":"K. Khudiakova, J. Maas, F. Pedrotti, The Annals of Applied Probability 35 (2025) 1913–1940.","ista":"Khudiakova K, Maas J, Pedrotti F. 2025. L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. The Annals of Applied Probability. 35(3), 1913–1940."},"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2402.04151"}],"publisher":"Institute of Mathematical Statistics"},{"ec_funded":1,"department":[{"_id":"JaMa"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"20591","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"25","corr_author":"1","OA_place":"publisher","publication":"Electronic Communications in Probability","year":"2025","DOAJ_listed":"1","date_created":"2025-11-02T23:01:35Z","article_type":"original","file_date_updated":"2025-11-04T07:34:05Z","author":[{"first_name":"Giovanni","last_name":"Brigati","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","full_name":"Brigati, Giovanni"},{"id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","full_name":"Pedrotti, Francesco","first_name":"Francesco","last_name":"Pedrotti"}],"language":[{"iso":"eng"}],"ddc":["500"],"doi":"10.1214/25-ECP717","file":[{"relation":"main_file","date_updated":"2025-11-04T07:34:05Z","content_type":"application/pdf","file_size":278078,"file_id":"20596","success":1,"date_created":"2025-11-04T07:34:05Z","access_level":"open_access","file_name":"2025_ElectronJourProbab_Brigati.pdf","creator":"dernst","checksum":"67858edbd74658fe38955fa1216f2f18"}],"project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020"}],"publication_status":"published","oa":1,"intvolume":"        30","oa_version":"Published Version","article_number":"71","scopus_import":"1","abstract":[{"lang":"eng","text":"In this paper we derive estimates for the Hessian of the logarithm (log-Hessian) for solutions to the heat equation. For initial data in the form of log-Lipschitz perturbation of strongly log-concave measures, the log-Hessian admits an explicit, uniform (in space) lower bound. This yields a new estimate for the Lipschitz constant of a transport map pushing forward the standard Gaussian to a measure in this class. On the other hand, we show that assuming only fast decay of the tails of the initial datum does not suffice to guarantee uniform log-Hessian upper bounds."}],"citation":{"ama":"Brigati G, Pedrotti F. Heat flow, log-concavity, and Lipschitz transport maps. <i>Electronic Communications in Probability</i>. 2025;30. doi:<a href=\"https://doi.org/10.1214/25-ECP717\">10.1214/25-ECP717</a>","ieee":"G. Brigati and F. Pedrotti, “Heat flow, log-concavity, and Lipschitz transport maps,” <i>Electronic Communications in Probability</i>, vol. 30. Institute of Mathematical Statistics, 2025.","ista":"Brigati G, Pedrotti F. 2025. Heat flow, log-concavity, and Lipschitz transport maps. Electronic Communications in Probability. 30, 71.","short":"G. Brigati, F. Pedrotti, Electronic Communications in Probability 30 (2025).","mla":"Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” <i>Electronic Communications in Probability</i>, vol. 30, 71, Institute of Mathematical Statistics, 2025, doi:<a href=\"https://doi.org/10.1214/25-ECP717\">10.1214/25-ECP717</a>.","chicago":"Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/25-ECP717\">https://doi.org/10.1214/25-ECP717</a>.","apa":"Brigati, G., &#38; Pedrotti, F. (2025). Heat flow, log-concavity, and Lipschitz transport maps. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/25-ECP717\">https://doi.org/10.1214/25-ECP717</a>"},"publisher":"Institute of Mathematical Statistics","OA_type":"gold","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"17353"}]},"publication_identifier":{"eissn":["1083-589X"]},"type":"journal_article","status":"public","volume":30,"title":"Heat flow, log-concavity, and Lipschitz transport maps","PlanS_conform":"1","isi":1,"acknowledgement":"This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/F65 and by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101034413. The authors thank Professors Jean Dolbeault, Jan Maas, and Nikita Simonov for many useful comments, and Professors Kazuhiro Ishige, Asuka Takatsu, and Yair Shenfeld for inspiring interactions.","arxiv":1,"date_published":"2025-09-25T00:00:00Z","article_processing_charge":"Yes","external_id":{"isi":["001611557000018"],"arxiv":["2404.15205"]},"date_updated":"2025-12-01T15:08:54Z","quality_controlled":"1","month":"09"},{"year":"2025","date_created":"2025-10-28T13:12:08Z","language":[{"iso":"eng"}],"author":[{"full_name":"Brigati, Giovanni","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","last_name":"Brigati","first_name":"Giovanni"},{"first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan"},{"first_name":"Filippo","last_name":"Quattrocchi","orcid":"0009-0000-9773-1931","id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308","full_name":"Quattrocchi, Filippo"}],"oa":1,"publication_status":"draft","doi":"10.48550/arXiv.2502.15665","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413"}],"_id":"20569","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"ec_funded":1,"day":"10","publication":"arXiv","corr_author":"1","OA_place":"repository","date_published":"2025-08-10T00:00:00Z","arxiv":1,"article_processing_charge":"No","acknowledgement":"This work was partially inspired by an unpublished note from 2014 by Guillaume Carlier,\r\nJean Dolbeault, and Bruno Nazaret. GB deeply thanks Jean Dolbeault for proposing\r\nthis problem to him, guiding him into the subject, and sharing the aforementioned note.\r\nWe are grateful to Karthik Elamvazhuthi for making us aware of the work [20].\r\nThe work of GB has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement\r\nNo 101034413.\r\nJM and FQ gratefully acknowledge support from the Austrian Science Fund (FWF)\r\nproject 10.55776/F65.","title":"Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between probability measures","date_updated":"2026-08-07T22:31:03Z","external_id":{"arxiv":["2502.15665"]},"month":"08","article_number":"2502.15665","citation":{"ama":"Brigati G, Maas J, Quattrocchi F. Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between probability measures. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2502.15665\">10.48550/arXiv.2502.15665</a>","ieee":"G. Brigati, J. Maas, and F. Quattrocchi, “Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between probability measures,” <i>arXiv</i>. .","ista":"Brigati G, Maas J, Quattrocchi F. Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between probability measures. arXiv, 2502.15665.","short":"G. Brigati, J. Maas, F. Quattrocchi, ArXiv (n.d.).","mla":"Brigati, Giovanni, et al. “Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-Order Discrepancies between Probability Measures.” <i>ArXiv</i>, 2502.15665, doi:<a href=\"https://doi.org/10.48550/arXiv.2502.15665\">10.48550/arXiv.2502.15665</a>.","chicago":"Brigati, Giovanni, Jan Maas, and Filippo Quattrocchi. “Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-Order Discrepancies between Probability Measures.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2502.15665\">https://doi.org/10.48550/arXiv.2502.15665</a>.","apa":"Brigati, G., Maas, J., &#38; Quattrocchi, F. (n.d.). Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between probability measures. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2502.15665\">https://doi.org/10.48550/arXiv.2502.15665</a>"},"keyword":["optimal transport","kinetic theory","second-order discrepancy","Vlasov equation","Wasserstein splines."],"abstract":[{"lang":"eng","text":"This is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framework naturally applies in biology, computer vision, and engineering. The central object of our study is a new discrepancy d between two probability distributions in position and velocity states, which is reminiscent of the 2-Wasserstein distance, but of second-order nature. We construct d in two steps. First, we optimise over transport plans. The cost function is given by the minimal acceleration between two coupled states on a fixed time horizon T. Second, we further optimise over the time horizon T > 0. We prove the existence of optimal transport plans and maps, and study two time-continuous characterisations of d. One is given in terms of dynamical transport plans. The other one -- in the spirit of the Benamou--Brenier formula -- is formulated as the minimisation of an action of the acceleration field, constrained by Vlasov's equations. Equivalence of static and dynamical formulations of d holds true. While part of this result can be derived from recent, parallel developments in optimal control between measures, we give an original proof relying on two new ingredients: Galilean regularisation of Vlasov's equations and a kinetic Monge--Mather shortening principle. Finally, we establish a first-order differential calculus in the geometry induced by d, and identify solutions to Vlasov's equations with curves of measures satisfying a certain d-absolute continuity condition. One consequence is an explicit formula for the d-derivative of such curves."}],"oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2502.15665","open_access":"1"}],"OA_type":"green","related_material":{"record":[{"status":"public","id":"20563","relation":"dissertation_contains"}]},"status":"public","type":"preprint"},{"publication_identifier":{"issn":["0941-0643"],"eissn":["1433-3058"]},"type":"journal_article","status":"public","publisher":"Springer Nature","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We investigate the potential of Multi-Objective, Deep Reinforcement Learning for stock and cryptocurrency single-asset trading: in particular, we consider a Multi-Objective algorithm which generalizes the reward functions and discount factor (i.e., these components are not specified a priori, but incorporated in the learning process). Firstly, using several important assets (BTCUSD, ETHUSDT, XRPUSDT, AAPL, SPY, NIFTY50), we verify the reward generalization property of the proposed Multi-Objective algorithm, and provide preliminary statistical evidence showing increased predictive stability over the corresponding Single-Objective strategy. Secondly, we show that the Multi-Objective algorithm has a clear edge over the corresponding Single-Objective strategy when the reward mechanism is sparse (i.e., when non-null feedback is infrequent over time). Finally, we discuss the generalization properties with respect to the discount factor. The entirety of our code is provided in open-source format."}],"citation":{"ieee":"F. Cornalba, C. Disselkamp, D. Scassola, and C. Helf, “Multi-objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading,” <i>Neural Computing and Applications</i>, vol. 36, no. 2. Springer Nature, pp. 617–637, 2024.","ama":"Cornalba F, Disselkamp C, Scassola D, Helf C. Multi-objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading. <i>Neural Computing and Applications</i>. 2024;36(2):617-637. doi:<a href=\"https://doi.org/10.1007/s00521-023-09033-7\">10.1007/s00521-023-09033-7</a>","apa":"Cornalba, F., Disselkamp, C., Scassola, D., &#38; Helf, C. (2024). Multi-objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading. <i>Neural Computing and Applications</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00521-023-09033-7\">https://doi.org/10.1007/s00521-023-09033-7</a>","chicago":"Cornalba, Federico, Constantin Disselkamp, Davide Scassola, and Christopher Helf. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.” <i>Neural Computing and Applications</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00521-023-09033-7\">https://doi.org/10.1007/s00521-023-09033-7</a>.","mla":"Cornalba, Federico, et al. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.” <i>Neural Computing and Applications</i>, vol. 36, no. 2, Springer Nature, 2024, pp. 617–37, doi:<a href=\"https://doi.org/10.1007/s00521-023-09033-7\">10.1007/s00521-023-09033-7</a>.","short":"F. Cornalba, C. Disselkamp, D. Scassola, C. Helf, Neural Computing and Applications 36 (2024) 617–637.","ista":"Cornalba F, Disselkamp C, Scassola D, Helf C. 2024. Multi-objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications. 36(2), 617–637."},"scopus_import":"1","month":"01","external_id":{"arxiv":["2203.04579"],"pmid":["38187995"]},"quality_controlled":"1","date_updated":"2025-04-23T07:39:14Z","title":"Multi-objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading","acknowledgement":"Open access funding provided by Università degli Studi di Trieste within the CRUI-CARE Agreement. Funding was provided by Austrian Science Fund (Grant No. F65), Horizon 2020 (Grant No. 754411) and Österreichische Forschungsförderungsgesellschaft.","arxiv":1,"article_processing_charge":"Yes (via OA deal)","date_published":"2024-01-01T00:00:00Z","volume":36,"corr_author":"1","publication":"Neural Computing and Applications","day":"01","page":"617-637","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"department":[{"_id":"JuFi"}],"issue":"2","ec_funded":1,"_id":"14451","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","pmid":1,"file":[{"file_name":"2024_NeuralCompApplications_Cornalba.pdf","access_level":"open_access","checksum":"04573d8e74c6119b97c2ca0a984e19a1","creator":"dernst","success":1,"file_id":"17251","date_created":"2024-07-16T08:08:54Z","date_updated":"2024-07-16T08:08:54Z","relation":"main_file","content_type":"application/pdf","file_size":4412285}],"project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"doi":"10.1007/s00521-023-09033-7","oa":1,"publication_status":"published","intvolume":"        36","file_date_updated":"2024-07-16T08:08:54Z","author":[{"orcid":"0000-0002-6269-5149","last_name":"Cornalba","first_name":"Federico","full_name":"Cornalba, Federico","id":"2CEB641C-A400-11E9-A717-D712E6697425"},{"last_name":"Disselkamp","first_name":"Constantin","full_name":"Disselkamp, Constantin"},{"full_name":"Scassola, Davide","first_name":"Davide","last_name":"Scassola"},{"first_name":"Christopher","last_name":"Helf","full_name":"Helf, Christopher"}],"language":[{"iso":"eng"}],"ddc":["000"],"date_created":"2023-10-22T22:01:16Z","article_type":"original","year":"2024"},{"oa":1,"publication_status":"published","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"doi":"10.1007/s00332-023-10005-3","intvolume":"        34","language":[{"iso":"eng"}],"author":[{"first_name":"Elisa","last_name":"Davoli","full_name":"Davoli, Elisa"},{"full_name":"D’Elia, Lorenza","last_name":"D’Elia","first_name":"Lorenza"},{"last_name":"Ingmanns","first_name":"Jonas","id":"71523d30-15b2-11ec-abd3-f80aa909d6b0","full_name":"Ingmanns, Jonas"}],"date_created":"2024-01-28T23:01:42Z","article_type":"original","year":"2024","publication":"Journal of Nonlinear Science","day":"23","_id":"14884","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","department":[{"_id":"JuFi"}],"issue":"2","month":"01","external_id":{"isi":["001147480200001"],"arxiv":["2306.05151"]},"quality_controlled":"1","date_updated":"2025-09-04T11:54:01Z","title":"Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions","article_processing_charge":"No","arxiv":1,"date_published":"2024-01-23T00:00:00Z","isi":1,"acknowledgement":"All authors acknowledge support of the Austrian Science Fund (FWF) through the SFB project F65. The research of E. Davoli and L. D’Elia has additionally been supported by the FWF through grants V662, Y1292, and P35359, as well as from OeAD through the WTZ grant CZ09/2023.","volume":34,"type":"journal_article","publication_identifier":{"eissn":["1432-1467"],"issn":["0938-8974"]},"status":"public","publisher":"Springer Nature","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2306.05151"}],"article_number":"30","scopus_import":"1","citation":{"chicago":"Davoli, Elisa, Lorenza D’Elia, and Jonas Ingmanns. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” <i>Journal of Nonlinear Science</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00332-023-10005-3\">https://doi.org/10.1007/s00332-023-10005-3</a>.","apa":"Davoli, E., D’Elia, L., &#38; Ingmanns, J. (2024). Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. <i>Journal of Nonlinear Science</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00332-023-10005-3\">https://doi.org/10.1007/s00332-023-10005-3</a>","short":"E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024).","ista":"Davoli E, D’Elia L, Ingmanns J. 2024. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 34(2), 30.","mla":"Davoli, Elisa, et al. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” <i>Journal of Nonlinear Science</i>, vol. 34, no. 2, 30, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00332-023-10005-3\">10.1007/s00332-023-10005-3</a>.","ieee":"E. Davoli, L. D’Elia, and J. Ingmanns, “Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions,” <i>Journal of Nonlinear Science</i>, vol. 34, no. 2. Springer Nature, 2024.","ama":"Davoli E, D’Elia L, Ingmanns J. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. <i>Journal of Nonlinear Science</i>. 2024;34(2). doi:<a href=\"https://doi.org/10.1007/s00332-023-10005-3\">10.1007/s00332-023-10005-3</a>"},"abstract":[{"text":"We perform a stochastic homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and ergodicity, we characterize the Gamma-limit of a micromagnetic energy functional defined on magnetizations taking value in the unit sphere and including both symmetric and antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic energy functional with homogeneous coefficients. We provide explicit formulas for the effective magnetic properties of the composite material in terms of homogenization correctors. Additionally, the variational analysis of the two exchange energy terms is performed in the more general setting of functionals defined on manifold-valued maps with Sobolev regularity, in the case in which the target manifold is a bounded, orientable smooth surface with tubular neighborhood of uniform thickness. Eventually, we present an explicit characterization of minimizers of the effective exchange in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s predictions on the emergence of helical structures in composite ferromagnetic materials with stochastic microstructure.","lang":"eng"}],"oa_version":"Preprint"},{"OA_type":"hybrid","type":"journal_article","publication_identifier":{"eissn":["1572-929X"],"issn":["0926-2601"]},"status":"public","scopus_import":"1","citation":{"ieee":"L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random Riemannian geometry,” <i>Potential Analysis</i>, vol. 61. Springer Nature, pp. 501–553, 2024.","ama":"Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian geometry. <i>Potential Analysis</i>. 2024;61:501-553. doi:<a href=\"https://doi.org/10.1007/s11118-023-10118-0\">10.1007/s11118-023-10118-0</a>","chicago":"Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery Tour in Random Riemannian Geometry.” <i>Potential Analysis</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s11118-023-10118-0\">https://doi.org/10.1007/s11118-023-10118-0</a>.","apa":"Dello Schiavo, L., Kopfer, E., &#38; Sturm, K. T. (2024). A discovery tour in random Riemannian geometry. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-023-10118-0\">https://doi.org/10.1007/s11118-023-10118-0</a>","ista":"Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian geometry. Potential Analysis. 61, 501–553.","short":"L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis 61 (2024) 501–553.","mla":"Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.” <i>Potential Analysis</i>, vol. 61, Springer Nature, 2024, pp. 501–53, doi:<a href=\"https://doi.org/10.1007/s11118-023-10118-0\">10.1007/s11118-023-10118-0</a>."},"abstract":[{"text":"We study random perturbations of a Riemannian manifold (M, g) by means of so-called\r\nFractional Gaussian Fields, which are defined intrinsically by the given manifold. The fields\r\nh• : ω \u0002→ hω will act on the manifold via the conformal transformation g \u0002→ gω := e2hω g.\r\nOur focus will be on the regular case with Hurst parameter H > 0, the critical case H = 0\r\nbeing the celebrated Liouville geometry in two dimensions. We want to understand how basic\r\ngeometric and functional-analytic quantities like diameter, volume, heat kernel, Brownian\r\nmotion, spectral bound, or spectral gap change under the influence of the noise. And if so, is\r\nit possible to quantify these dependencies in terms of key parameters of the noise? Another\r\ngoal is to define and analyze in detail the Fractional Gaussian Fields on a general Riemannian\r\nmanifold, a fascinating object of independent interest.","lang":"eng"}],"oa_version":"Published Version","publisher":"Springer Nature","external_id":{"arxiv":["2012.06796"],"isi":["001151118800001"]},"date_updated":"2025-09-04T11:57:14Z","quality_controlled":"1","month":"10","volume":61,"title":"A discovery tour in random Riemannian geometry","arxiv":1,"date_published":"2024-10-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","acknowledgement":"The authors would like to thank Matthias Erbar and Ronan Herry for valuable discussions on this project. They are also grateful to Nathanaël Berestycki, and Fabrice Baudoin for respectively pointing out the references [7], and [6, 24], and to Julien Fageot and Thomas Letendre for pointing out a mistake in a previous version of the proof of Proposition 3.10. The authors feel very much indebted to an anonymous reviewer for his/her careful reading and the many valuable suggestions that have significantly contributed to the improvement of the paper. L.D.S. gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft through CRC 1060 as well as through SPP 2265, and by the Austrian Science Fund (FWF) grant F65 at Institute of Science and Technology Austria. This research was funded in whole or in part by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. E.K. and K.-T.S. gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft through the Hausdorff Center for Mathematics and through CRC 1060 as well as through SPP 2265.\r\nOpen Access funding enabled and organized by Projekt DEAL.","isi":1,"day":"01","OA_place":"publisher","publication":"Potential Analysis","_id":"14934","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","department":[{"_id":"JaMa"}],"page":"501-553","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","file_date_updated":"2025-01-09T08:13:34Z","ddc":["510"],"language":[{"iso":"eng"}],"author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870"},{"full_name":"Kopfer, Eva","last_name":"Kopfer","first_name":"Eva"},{"full_name":"Sturm, Karl Theodor","first_name":"Karl Theodor","last_name":"Sturm"}],"oa":1,"publication_status":"published","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"doi":"10.1007/s11118-023-10118-0","file":[{"file_size":1294993,"date_updated":"2025-01-09T08:13:34Z","content_type":"application/pdf","relation":"main_file","date_created":"2025-01-09T08:13:34Z","success":1,"file_id":"18789","creator":"dernst","checksum":"33c688bdf296c3d8f8bbd96c7dd26037","file_name":"2024_PotentialAnalysis_DelloSchiavo.pdf","access_level":"open_access"}],"intvolume":"        61","year":"2024","date_created":"2024-02-04T23:00:54Z","article_type":"original"},{"day":"01","publication":"Annals of Applied Probability","corr_author":"1","issue":"2","department":[{"_id":"JaMa"}],"ec_funded":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"15317","page":"1789-1845","author":[{"full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","last_name":"Dello Schiavo"},{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","full_name":"Portinale, Lorenzo","last_name":"Portinale","first_name":"Lorenzo"},{"last_name":"Sau","first_name":"Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425","full_name":"Sau, Federico"}],"language":[{"iso":"eng"}],"intvolume":"        34","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"},{"grant_number":"M03211","_id":"3490b268-11ca-11ed-8bc3-e0ad03f48839","name":"Reaching consensus in heterogeneous random opinion dynamics"},{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"name":"Configuration Spaces over Non-Smooth Spaces","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208"},{"_id":"260788DE-B435-11E9-9278-68D0E5697425","grant_number":"W1245","call_identifier":"FWF","name":"Dissipation and dispersion in nonlinear partial differential equations"}],"doi":"10.1214/23-AAP2007","oa":1,"publication_status":"published","year":"2024","article_type":"original","date_created":"2024-04-14T22:01:02Z","status":"public","publication_identifier":{"issn":["1050-5164"]},"type":"journal_article","oa_version":"Preprint","scopus_import":"1","abstract":[{"text":"We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes on a bounded Lipschitz domain Ω, with both fast and slow boundary. For the random walks on Ω dual to SEP/SIP we establish: a functional-CLT-type convergence to the Brownian motion on Ω with either Neumann (slow boundary), Dirichlet (fast boundary), or Robin (at criticality) boundary conditions; the discrete-to-continuum convergence of the corresponding harmonic profiles. As a consequence, we rigorously derive the hydrodynamic and hydrostatic limits for SEP/SIP on Ω, and analyze their stationary nonequilibrium fluctuations. All scaling limit results for SEP/SIP concern finite-dimensional distribution convergence only, as our duality techniques do not require to establish tightness for the fields associated to the particle systems.","lang":"eng"}],"citation":{"ieee":"L. Dello Schiavo, L. Portinale, and F. Sau, “Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains,” <i>Annals of Applied Probability</i>, vol. 34, no. 2. Institute of Mathematical Statistics, pp. 1789–1845, 2024.","ama":"Dello Schiavo L, Portinale L, Sau F. Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains. <i>Annals of Applied Probability</i>. 2024;34(2):1789-1845. doi:<a href=\"https://doi.org/10.1214/23-AAP2007\">10.1214/23-AAP2007</a>","chicago":"Dello Schiavo, Lorenzo, Lorenzo Portinale, and Federico Sau. “Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Nonequilibrium States in Lipschitz Domains.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2024. <a href=\"https://doi.org/10.1214/23-AAP2007\">https://doi.org/10.1214/23-AAP2007</a>.","apa":"Dello Schiavo, L., Portinale, L., &#38; Sau, F. (2024). Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-AAP2007\">https://doi.org/10.1214/23-AAP2007</a>","ista":"Dello Schiavo L, Portinale L, Sau F. 2024. Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains. Annals of Applied Probability. 34(2), 1789–1845.","short":"L. Dello Schiavo, L. Portinale, F. Sau, Annals of Applied Probability 34 (2024) 1789–1845.","mla":"Dello Schiavo, Lorenzo, et al. “Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Nonequilibrium States in Lipschitz Domains.” <i>Annals of Applied Probability</i>, vol. 34, no. 2, Institute of Mathematical Statistics, 2024, pp. 1789–845, doi:<a href=\"https://doi.org/10.1214/23-AAP2007\">10.1214/23-AAP2007</a>."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2112.14196"}],"publisher":"Institute of Mathematical Statistics","date_updated":"2025-09-04T13:36:00Z","quality_controlled":"1","external_id":{"arxiv":["2112.14196"],"isi":["001198623200016"]},"month":"04","volume":34,"acknowledgement":"The first author gratefully acknowledges funding by the Austrian Science Fund (FWF) grant F65, by the European Research Council (ERC, grant agreement No 716117, awarded to Prof. Dr. Jan Maas). He also gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) grant ESPRIT 208.\r\nThe second author gratefully acknowledges funding by the Hausdorff Center for Mathematics at the University of Bonn. Part of this work was completed while this author was a member of the Institute of Science and Technology Austria. He gratefully acknowledges funding of his position at that time by the Austrian Science Fund (FWF) grants F65 and W1245.\r\nThe third author gratefully acknowledges funding by the Lise Meitner fellowship, Austrian Science Fund (FWF): M3211. Part of this work was completed while funded by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.","isi":1,"arxiv":1,"article_processing_charge":"No","date_published":"2024-04-01T00:00:00Z","title":"Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains"},{"page":"3779-3804","ec_funded":1,"department":[{"_id":"JaMa"}],"issue":"6","_id":"17143","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication":"Transactions of the American Mathematical Society","day":"01","article_type":"original","date_created":"2024-06-16T22:01:06Z","year":"2024","intvolume":"       377","doi":"10.1090/tran/9156","project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"}],"publication_status":"published","oa":1,"author":[{"last_name":"Dello Schiavo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338"},{"first_name":"Francesco","last_name":"Pedrotti","full_name":"Pedrotti, Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"}],"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2304.05239","open_access":"1"}],"publisher":"American Mathematical Society","oa_version":"Preprint","abstract":[{"text":"This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical Kurdyka–Łojasiewicz inequality for a large class of parameter functions. Our assumptions are given in terms of the initial data, without any reference to an equilibrium point. The main results are convergence statements for gradient flow curves and proximal point sequences to a global minimiser, together with sharp quantitative estimates on the speed of convergence. These convergence results apply in the general setting of lower semicontinuous functionals on complete metric spaces, generalising recent results for smooth functionals on Rn. While the non-smooth setting covers very general spaces, it is also useful for (non)-smooth functionals on Rn.\r\n.","lang":"eng"}],"scopus_import":"1","citation":{"ama":"Dello Schiavo L, Maas J, Pedrotti F. Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. <i>Transactions of the American Mathematical Society</i>. 2024;377(6):3779-3804. doi:<a href=\"https://doi.org/10.1090/tran/9156\">10.1090/tran/9156</a>","ieee":"L. Dello Schiavo, J. Maas, and F. Pedrotti, “Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces,” <i>Transactions of the American Mathematical Society</i>, vol. 377, no. 6. American Mathematical Society, pp. 3779–3804, 2024.","short":"L. Dello Schiavo, J. Maas, F. Pedrotti, Transactions of the American Mathematical Society 377 (2024) 3779–3804.","ista":"Dello Schiavo L, Maas J, Pedrotti F. 2024. Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. Transactions of the American Mathematical Society. 377(6), 3779–3804.","mla":"Dello Schiavo, Lorenzo, et al. “Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces.” <i>Transactions of the American Mathematical Society</i>, vol. 377, no. 6, American Mathematical Society, 2024, pp. 3779–804, doi:<a href=\"https://doi.org/10.1090/tran/9156\">10.1090/tran/9156</a>.","chicago":"Dello Schiavo, Lorenzo, Jan Maas, and Francesco Pedrotti. “Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2024. <a href=\"https://doi.org/10.1090/tran/9156\">https://doi.org/10.1090/tran/9156</a>.","apa":"Dello Schiavo, L., Maas, J., &#38; Pedrotti, F. (2024). Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/9156\">https://doi.org/10.1090/tran/9156</a>"},"status":"public","publication_identifier":{"issn":["0002-9947"],"eissn":["1088-6850"]},"type":"journal_article","related_material":{"record":[{"status":"public","id":"17336","relation":"dissertation_contains"}]},"acknowledgement":"The authors gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 716117). This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/ESP208. This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/F65","isi":1,"date_published":"2024-06-01T00:00:00Z","article_processing_charge":"No","arxiv":1,"title":"Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces","volume":377,"month":"06","quality_controlled":"1","date_updated":"2026-04-07T13:00:02Z","external_id":{"arxiv":["2304.05239"],"isi":["001203273300001"]}},{"external_id":{"isi":["001351918100029"]},"quality_controlled":"1","date_updated":"2025-09-08T14:29:45Z","month":"11","volume":110,"title":"Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension","isi":1,"acknowledgement":"The authors are grateful to Masha Gordina for helpful references, and to Nathanaël Berestycki, Baptiste Cerclé, and Ewain Gwynne for valuable comments on the first circulated version of this paper. They also would like to thank Sebastian Andres, Peter Friz, and Yizheng Yuan for pointing out an erroneous formulation in the previous version of Theorem 5.7. Moreover, KTS would liketo express his thanks to Sebastian Andres, Matthias Erbar, Martin Huesmann, and Jan Mass for stimulating discussions on previous attempts to this project. LDS gratefully acknowledges financial support from the European Research Council (grant agreement No 716117, awarded to J. Maas), from the Austrian Science Fund (FWF) project 10.55776/ESP208, and from the Austrian Science Fund (FWF) project 10.55776/F65.RH, EK, and KTS gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft through the project “Random Riemannian Geometry” within the SPP 2265 “Random Geomet-ric Systems,” through the Hausdorff Center for Mathematics (project ID 390685813), and through project B03 within the CRC 1060 (project ID 211504053). RH and KTS also gratefully acknowledge financial support from the European Research Council through the ERC AdG “RicciBounds”(grant agreement 694405).Data sharing not applicable to this article as no datasets were generated or analyzed during the current study. Open access funding enabled and organized by Projekt DEAL.","article_processing_charge":"Yes (via OA deal)","date_published":"2024-11-01T00:00:00Z","OA_type":"hybrid","publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"type":"journal_article","status":"public","oa_version":"Published Version","article_number":"e70003","scopus_import":"1","abstract":[{"lang":"eng","text":"For large classes of even-dimensional Riemannian manifolds (Formula presented.), we construct and analyze conformally invariant random fields. These centered Gaussian fields (Formula presented.), called co-polyharmonic Gaussian fields, are characterized by their covariance kernels k which exhibit a precise logarithmic divergence: (Formula presented.). They share a fundamental quasi-invariance property under conformal transformations. In terms of the co-polyharmonic Gaussian field (Formula presented.), we define the Liouville Quantum Gravity measure, a random measure on (Formula presented.), heuristically given as (Formula presented.) and rigorously obtained as almost sure weak limit of the right-hand side with (Formula presented.) replaced by suitable regular approximations (Formula presented.). In terms on the Liouville Quantum Gravity measure, we define the Liouville Brownian motion on (Formula presented.) and the random GJMS operators. Finally, we present an approach to a conformal field theory in arbitrary even dimension with an ansatz based on Branson's (Formula presented.) -curvature: we give a rigorous meaning to the Polyakov–Liouville measure (Formula presented.) and we derive the corresponding conformal anomaly. The set of admissible manifolds is conformally invariant. It includes all compact 2-dimensional Riemannian manifolds, all compact non-negatively curved Einstein manifolds of even dimension, and large classes of compact hyperbolic manifolds of even dimension. However, not every compact even-dimensional Riemannian manifold is admissible. Our results concerning the logarithmic divergence of the kernel (Formula presented.) rely on new sharp estimates for heat kernels and higher order Green kernels on arbitrary closed manifolds. "}],"citation":{"apa":"Dello Schiavo, L., Herry, R., Kopfer, E., &#38; Sturm, K. T. (2024). Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension. <i>Journal of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/jlms.70003\">https://doi.org/10.1112/jlms.70003</a>","chicago":"Dello Schiavo, Lorenzo, Ronan Herry, Eva Kopfer, and Karl Theodor Sturm. “Conformally Invariant Random Fields, Liouville Quantum Gravity Measures, and Random Paneitz Operators on Riemannian Manifolds of Even Dimension.” <i>Journal of the London Mathematical Society</i>. London Mathematical Society, 2024. <a href=\"https://doi.org/10.1112/jlms.70003\">https://doi.org/10.1112/jlms.70003</a>.","mla":"Dello Schiavo, Lorenzo, et al. “Conformally Invariant Random Fields, Liouville Quantum Gravity Measures, and Random Paneitz Operators on Riemannian Manifolds of Even Dimension.” <i>Journal of the London Mathematical Society</i>, vol. 110, no. 5, e70003, London Mathematical Society, 2024, doi:<a href=\"https://doi.org/10.1112/jlms.70003\">10.1112/jlms.70003</a>.","short":"L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Journal of the London Mathematical Society 110 (2024).","ista":"Dello Schiavo L, Herry R, Kopfer E, Sturm KT. 2024. Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension. Journal of the London Mathematical Society. 110(5), e70003.","ieee":"L. Dello Schiavo, R. Herry, E. Kopfer, and K. T. Sturm, “Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension,” <i>Journal of the London Mathematical Society</i>, vol. 110, no. 5. London Mathematical Society, 2024.","ama":"Dello Schiavo L, Herry R, Kopfer E, Sturm KT. Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension. <i>Journal of the London Mathematical Society</i>. 2024;110(5). doi:<a href=\"https://doi.org/10.1112/jlms.70003\">10.1112/jlms.70003</a>"},"publisher":"London Mathematical Society","file_date_updated":"2024-11-04T08:54:26Z","author":[{"full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","last_name":"Dello Schiavo"},{"full_name":"Herry, Ronan","last_name":"Herry","first_name":"Ronan"},{"full_name":"Kopfer, Eva","last_name":"Kopfer","first_name":"Eva"},{"first_name":"Karl Theodor","last_name":"Sturm","full_name":"Sturm, Karl Theodor"}],"ddc":["510"],"language":[{"iso":"eng"}],"file":[{"date_created":"2024-11-04T08:54:26Z","success":1,"file_id":"18497","creator":"dernst","checksum":"143816823b5f43bd3748da8e3e91cef5","file_name":"2024_JourLondonMathSoc_Schiavo.pdf","access_level":"open_access","file_size":911476,"date_updated":"2024-11-04T08:54:26Z","content_type":"application/pdf","relation":"main_file"}],"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"},{"name":"Configuration Spaces over Non-Smooth Spaces","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"doi":"10.1112/jlms.70003","oa":1,"publication_status":"published","intvolume":"       110","year":"2024","date_created":"2024-11-03T23:01:44Z","article_type":"original","day":"01","OA_place":"publisher","publication":"Journal of the London Mathematical Society","issue":"5","ec_funded":1,"department":[{"_id":"JaMa"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"18490","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}},{"author":[{"full_name":"Pedrotti, Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","first_name":"Francesco","last_name":"Pedrotti"},{"orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"id":"27EB676C-8706-11E9-9510-7717E6697425","full_name":"Mondelli, Marco","last_name":"Mondelli","first_name":"Marco","orcid":"0000-0002-3242-7020"}],"language":[{"iso":"eng"}],"ddc":["000"],"file_date_updated":"2025-01-27T12:19:44Z","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"name":"Prix Lopez-Loretta 2019 - Marco Mondelli","_id":"059876FA-7A3F-11EA-A408-12923DDC885E"}],"file":[{"file_name":"2024_TMLR_Pedrotti.pdf","access_level":"open_access","checksum":"76a1fd5afd8ee6f7ae0e5912d7dbf6b4","creator":"dernst","success":1,"file_id":"18898","date_created":"2025-01-27T12:19:44Z","content_type":"application/pdf","date_updated":"2025-01-27T12:19:44Z","relation":"main_file","file_size":780315}],"publication_status":"published","oa":1,"year":"2024","alternative_title":["TMLR"],"date_created":"2025-01-27T12:18:05Z","day":"01","publication":"Transactions on Machine Learning Research","corr_author":"1","OA_place":"publisher","department":[{"_id":"JaMa"},{"_id":"MaMo"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"18897","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2025-04-15T08:31:35Z","quality_controlled":"1","external_id":{"arxiv":["2305.14164"]},"month":"06","acknowledgement":"Francesco Pedrotti and Jan Maas acknowledge support by the Austrian Science Fund (FWF) project 10.55776/F65. Marco Mondelli acknowledges support by the 2019 Lopez-Loreta prize.\r\n","date_published":"2024-06-01T00:00:00Z","article_processing_charge":"No","arxiv":1,"title":"Improved convergence of score-based diffusion models via prediction-correction","OA_type":"gold","related_material":{"record":[{"relation":"earlier_version","id":"17350","status":"public"}]},"status":"public","publication_identifier":{"issn":["2835-8856"]},"type":"conference","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time T1 by adding noise to the data, (ii) estimate its score function, and (iii) use such estimate to run a reverse process. As the reverse process is initialized with the stationary distribution of the forward one, the existing analysis paradigm requires T1→∞. This is however problematic: from a theoretical viewpoint, for a given precision of the score approximation, the convergence guarantee fails as T1 diverges; from a practical viewpoint, a large T1 increases computational costs and leads to error propagation. This paper addresses the issue by considering a version of the popular predictor-corrector scheme: after running the forward process, we first estimate the final distribution via an inexact Langevin dynamics and then revert the process. Our key technical contribution is to provide convergence guarantees which require to run the forward process only for a fixed finite time T1. Our bounds exhibit a mild logarithmic dependence on the input dimension and the subgaussian norm of the target distribution, have minimal assumptions on the data, and require only to control the L2 loss on the score approximation, which is the quantity minimized in practice."}],"citation":{"chicago":"Pedrotti, Francesco, Jan Maas, and Marco Mondelli. “Improved Convergence of Score-Based Diffusion Models via Prediction-Correction.” In <i>Transactions on Machine Learning Research</i>, 2024.","apa":"Pedrotti, F., Maas, J., &#38; Mondelli, M. (2024). Improved convergence of score-based diffusion models via prediction-correction. In <i>Transactions on Machine Learning Research</i>.","short":"F. Pedrotti, J. Maas, M. Mondelli, in:, Transactions on Machine Learning Research, 2024.","ista":"Pedrotti F, Maas J, Mondelli M. 2024. Improved convergence of score-based diffusion models via prediction-correction. Transactions on Machine Learning Research. , TMLR, .","mla":"Pedrotti, Francesco, et al. “Improved Convergence of Score-Based Diffusion Models via Prediction-Correction.” <i>Transactions on Machine Learning Research</i>, 2024.","ieee":"F. Pedrotti, J. Maas, and M. Mondelli, “Improved convergence of score-based diffusion models via prediction-correction,” in <i>Transactions on Machine Learning Research</i>, 2024.","ama":"Pedrotti F, Maas J, Mondelli M. Improved convergence of score-based diffusion models via prediction-correction. In: <i>Transactions on Machine Learning Research</i>. ; 2024."},"scopus_import":"1"},{"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"17282","department":[{"_id":"JaMa"}],"issue":"6","ec_funded":1,"pmid":1,"corr_author":"1","publication":"Calculus of Variations and Partial Differential Equations","day":"01","date_created":"2024-07-21T22:01:01Z","article_type":"original","year":"2024","publication_status":"published","oa":1,"file":[{"date_created":"2024-07-22T07:05:32Z","success":1,"file_id":"17289","checksum":"a0cf0e0ba2157aabb287cb597be17dac","creator":"dernst","file_name":"2024_CalculusVariations_Brooks.pdf","access_level":"open_access","file_size":416622,"relation":"main_file","date_updated":"2024-07-22T07:05:32Z","content_type":"application/pdf"}],"project":[{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"doi":"10.1007/s00526-024-02755-z","intvolume":"        63","file_date_updated":"2024-07-22T07:05:32Z","ddc":["510"],"language":[{"iso":"eng"}],"author":[{"full_name":"Brooks, Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","orcid":"0000-0002-6249-0928","first_name":"Morris","last_name":"Brooks"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338"}],"publisher":"Springer Nature","scopus_import":"1","article_number":"153","citation":{"short":"M. Brooks, J. Maas, Calculus of Variations and Partial Differential Equations 63 (2024).","ista":"Brooks M, Maas J. 2024. Characterisation of gradient flows for a given functional. Calculus of Variations and Partial Differential Equations. 63(6), 153.","mla":"Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a given Functional.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 63, no. 6, 153, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00526-024-02755-z\">10.1007/s00526-024-02755-z</a>.","chicago":"Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a given Functional.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00526-024-02755-z\">https://doi.org/10.1007/s00526-024-02755-z</a>.","apa":"Brooks, M., &#38; Maas, J. (2024). Characterisation of gradient flows for a given functional. <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00526-024-02755-z\">https://doi.org/10.1007/s00526-024-02755-z</a>","ama":"Brooks M, Maas J. Characterisation of gradient flows for a given functional. <i>Calculus of Variations and Partial Differential Equations</i>. 2024;63(6). doi:<a href=\"https://doi.org/10.1007/s00526-024-02755-z\">10.1007/s00526-024-02755-z</a>","ieee":"M. Brooks and J. Maas, “Characterisation of gradient flows for a given functional,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 63, no. 6. Springer Nature, 2024."},"abstract":[{"text":"Let  X  be a vector field and  Y  be a co-vector field on a smooth manifold  M. Does there exist a smooth Riemannian metric  gαβ  on  M  such that  Yβ=gαβXα ? The main result of this note gives necessary and sufficient conditions for this to be true. As an application of this result we show that a finite-dimensional ergodic Lindblad equation admits a gradient flow structure for the von Neumann relative entropy if and only if the condition of BKM-detailed balance holds.","lang":"eng"}],"oa_version":"Published Version","type":"journal_article","publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"status":"public","title":"Characterisation of gradient flows for a given functional","date_published":"2024-07-01T00:00:00Z","arxiv":1,"article_processing_charge":"Yes (via OA deal)","isi":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).J. M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117), and by the Austrian Science Fund (FWF), Project SFB F65. We thank the anonymous referee for valuable comments on the paper.","volume":63,"month":"07","external_id":{"arxiv":["2209.11149"],"isi":["001258097800003"],"pmid":["38947856"]},"quality_controlled":"1","date_updated":"2025-09-08T08:24:51Z"},{"type":"dissertation","publication_identifier":{"issn":["2663-337X"]},"status":"public","related_material":{"record":[{"status":"public","id":"17351","relation":"part_of_dissertation"},{"id":"17353","relation":"part_of_dissertation","status":"public"},{"id":"17350","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","id":"17352","status":"public"},{"status":"public","id":"17143","relation":"part_of_dissertation"}]},"publisher":"Institute of Science and Technology Austria","citation":{"short":"F. Pedrotti, Functional Inequalities and Convergence of Stochastic Processes, Institute of Science and Technology Austria, 2024.","ista":"Pedrotti F. 2024. Functional inequalities and convergence of stochastic processes. Institute of Science and Technology Austria.","mla":"Pedrotti, Francesco. <i>Functional Inequalities and Convergence of Stochastic Processes</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:17336\">10.15479/at:ista:17336</a>.","chicago":"Pedrotti, Francesco. “Functional Inequalities and Convergence of Stochastic Processes.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:17336\">https://doi.org/10.15479/at:ista:17336</a>.","apa":"Pedrotti, F. (2024). <i>Functional inequalities and convergence of stochastic processes</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:17336\">https://doi.org/10.15479/at:ista:17336</a>","ama":"Pedrotti F. Functional inequalities and convergence of stochastic processes. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:17336\">10.15479/at:ista:17336</a>","ieee":"F. Pedrotti, “Functional inequalities and convergence of stochastic processes,” Institute of Science and Technology Austria, 2024."},"abstract":[{"text":"This thesis deals with the study of stochastic processes and their ergodicity properties. The\r\nvariety of problems encountered calls for a set of different approaches, ranging from classical to\r\nmodern ones: a special place is held by probabilistic methods based on couplings, by functional\r\ninequalities, and by the theory of gradient flows in the space of measures.\r\n\r\nThe material is organized as follows. Chapter 1 contains the introduction to this thesis, starting\r\nwith a general presentation of some of the relevant topics. Section 1.1 is dedicated to the\r\ntheory of gradient flows in metric spaces, and introduces the first contribution of this thesis\r\n[DSMP24], which is presented in detail in Chapter 2. Section 1.2 moves to the topic of\r\ncurvature of Markov chains, concluding with a brief description of our second contribution\r\n[Ped23], which is included in Chapter 3. Section 1.3 discusses applications of stochastic\r\nprocesses to the theory of sampling, in particular the recent framework of score-based diffusion\r\nmodels, and our contribution [PMM24], which is contained in Chapter 4. Section 1.4 discusses\r\nsome related problems, concerning the regularization properties of the heat flow. It serves\r\nas a motivation for the work [BP24], which we report in Chapter 5. Finally, Section 1.5\r\ndiscusses the last contribution of this thesis, which can be found in Chapter 6. It deals with\r\nthe convergence to equilibrium of a particular stochastic model from quantitative genetics:\r\nthis is established via some functional inequalities, which we prove with probabilistic arguments\r\nbased on couplings.\r\n","lang":"eng"}],"oa_version":"Published Version","month":"07","date_updated":"2026-04-07T13:00:03Z","title":"Functional inequalities and convergence of stochastic processes","article_processing_charge":"No","date_published":"2024-07-31T00:00:00Z","OA_place":"publisher","corr_author":"1","day":"31","page":"183","tmp":{"short":"CC BY-NC-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"supervisor":[{"orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"has_accepted_license":"1","_id":"17336","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","ec_funded":1,"department":[{"_id":"GradSch"},{"_id":"JaMa"}],"oa":1,"publication_status":"published","doi":"10.15479/at:ista:17336","file":[{"date_created":"2024-08-02T09:23:26Z","success":1,"file_id":"17366","checksum":"11650bab714ef85ad43a287060850523","creator":"fpedrott","file_name":"thesis_final.pdf","access_level":"open_access","file_size":2941599,"relation":"main_file","date_updated":"2024-08-02T09:23:26Z","content_type":"application/pdf"},{"access_level":"closed","file_name":"thesis_final_source.zip","checksum":"c30ba5611941226cf1bfc867c25b1e80","creator":"fpedrott","file_id":"17367","date_created":"2024-08-02T09:27:15Z","content_type":"application/x-zip-compressed","relation":"source_file","date_updated":"2024-08-02T09:27:15Z","file_size":6293375}],"project":[{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"file_date_updated":"2024-08-02T09:27:15Z","degree_awarded":"PhD","language":[{"iso":"eng"}],"ddc":["500","510","515","519"],"author":[{"full_name":"Pedrotti, Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","first_name":"Francesco","last_name":"Pedrotti"}],"date_created":"2024-07-29T09:14:14Z","alternative_title":["ISTA Thesis"],"year":"2024"}]