[{"external_id":{"arxiv":["2302.02963"],"isi":["001366948500001"]},"department":[{"_id":"JaMa"}],"citation":{"apa":"Dello Schiavo, L., Herry, R., Kopfer, E., & Sturm, K. T. (2025). Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous. Mathematische Nachrichten. Wiley. https://doi.org/10.1002/mana.202400169","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. Mathematische Nachrichten. 2025;298(1):244-281. doi:10.1002/mana.202400169","mla":"Dello Schiavo, Lorenzo, et al. “Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary Dimension: From Discrete to Continuous.” Mathematische Nachrichten, vol. 298, no. 1, Wiley, 2025, pp. 244–81, doi:10.1002/mana.202400169.","short":"L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Mathematische Nachrichten 298 (2025) 244–281.","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.","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.” Mathematische Nachrichten. Wiley, 2025. https://doi.org/10.1002/mana.202400169.","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,” Mathematische Nachrichten, vol. 298, no. 1. Wiley, pp. 244–281, 2025."},"publication_identifier":{"eissn":["1522-2616"],"issn":["0025-584X"]},"has_accepted_license":"1","OA_type":"hybrid","language":[{"iso":"eng"}],"OA_place":"publisher","issue":"1","article_processing_charge":"Yes (via OA deal)","date_updated":"2025-04-14T07:27:49Z","_id":"18632","publication":"Mathematische Nachrichten","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2025-01-13T10:34:42Z","intvolume":" 298","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.","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"publisher":"Wiley","publication_status":"published","oa_version":"Published Version","ec_funded":1,"date_published":"2025-01-01T00:00:00Z","volume":298,"doi":"10.1002/mana.202400169","year":"2025","project":[{"call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","name":"Configuration Spaces over Non-Smooth Spaces"}],"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","first_name":"Ronan","last_name":"Herry"},{"full_name":"Kopfer, Eva","first_name":"Eva","last_name":"Kopfer"},{"first_name":"Karl Theodor","last_name":"Sturm","full_name":"Sturm, Karl Theodor"}],"scopus_import":"1","page":"244-281","day":"01","article_type":"original","ddc":["510"],"month":"01","title":"Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous","abstract":[{"lang":"eng","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.). "}],"date_created":"2024-12-08T23:01:56Z","oa":1,"file":[{"file_size":1734511,"checksum":"1dc50d156feb777c86d779fb1c9ac875","file_id":"18838","relation":"main_file","date_updated":"2025-01-13T10:34:42Z","access_level":"open_access","creator":"dernst","content_type":"application/pdf","date_created":"2025-01-13T10:34:42Z","file_name":"2025_MathNachrichten_DelloSchiavo.pdf","success":1}],"type":"journal_article","arxiv":1,"quality_controlled":"1","status":"public"},{"OA_type":"green","OA_place":"repository","language":[{"iso":"eng"}],"external_id":{"isi":["001434322900006"],"arxiv":["2308.00516"]},"publication_identifier":{"issn":["1050-5164"]},"citation":{"apa":"Pedrotti, F. (2025). Contractive coupling rates and curvature lower bounds for Markov chains. The Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/24-aap2113","ista":"Pedrotti F. 2025. Contractive coupling rates and curvature lower bounds for Markov chains. The Annals of Applied Probability. 35(1), 196–250.","short":"F. Pedrotti, The Annals of Applied Probability 35 (2025) 196–250.","ama":"Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. The Annals of Applied Probability. 2025;35(1):196-250. doi:10.1214/24-aap2113","mla":"Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” The Annals of Applied Probability, vol. 35, no. 1, Institute of Mathematical Statistics, 2025, pp. 196–250, doi:10.1214/24-aap2113.","ieee":"F. Pedrotti, “Contractive coupling rates and curvature lower bounds for Markov chains,” The Annals of Applied Probability, vol. 35, no. 1. Institute of Mathematical Statistics, pp. 196–250, 2025.","chicago":"Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” The Annals of Applied Probability. Institute of Mathematical Statistics, 2025. https://doi.org/10.1214/24-aap2113."},"department":[{"_id":"JaMa"}],"date_updated":"2025-11-05T13:50:07Z","article_processing_charge":"No","_id":"20040","issue":"1","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,"publication":"The Annals of Applied Probability","intvolume":" 35","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"oa_version":"Preprint","date_published":"2025-02-01T00:00:00Z","volume":35,"publication_status":"published","publisher":"Institute of Mathematical Statistics","article_type":"original","author":[{"last_name":"Pedrotti","first_name":"Francesco","full_name":"Pedrotti, Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"}],"project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"doi":"10.1214/24-aap2113","year":"2025","day":"01","scopus_import":"1","page":"196 - 250","month":"02","title":"Contractive coupling rates and curvature lower bounds for Markov chains","related_material":{"record":[{"id":"17351","status":"public","relation":"earlier_version"}]},"oa":1,"type":"journal_article","abstract":[{"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.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2308.00516"}],"date_created":"2025-07-21T07:49:15Z","arxiv":1,"quality_controlled":"1","status":"public","corr_author":"1"},{"_id":"20814","article_processing_charge":"Yes (via OA deal)","date_updated":"2025-12-15T13:11:24Z","has_accepted_license":"1","OA_place":"publisher","OA_type":"hybrid","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"citation":{"ista":"Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. 2025. Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. Potential Analysis. 64, 6.","short":"M. Keller, D. Lenz, M. Schmidt, M. Schwarz, M. Wirth, Potential Analysis 64 (2025).","mla":"Keller, Matthias, et al. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” Potential Analysis, vol. 64, 6, Springer Nature, 2025, doi:10.1007/s11118-025-10251-y.","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. Potential Analysis. 2025;64. doi:10.1007/s11118-025-10251-y","apa":"Keller, M., Lenz, D., Schmidt, M., Schwarz, M., & Wirth, M. (2025). Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-025-10251-y","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,” Potential Analysis, vol. 64. Springer Nature, 2025.","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.” Potential Analysis. Springer Nature, 2025. https://doi.org/10.1007/s11118-025-10251-y."},"publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"external_id":{"arxiv":["2301.01035"]},"volume":64,"date_published":"2025-12-03T00:00:00Z","oa_version":"Published Version","ec_funded":1,"publisher":"Springer Nature","publication_status":"epub_ahead","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"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).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 64","publication":"Potential Analysis","title":"Boundary representations of intermediate forms between a regular Dirichlet form and its active main part","month":"12","PlanS_conform":"1","ddc":["510"],"article_type":"original","article_number":"6","scopus_import":"1","day":"03","doi":"10.1007/s11118-025-10251-y","year":"2025","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Gradient flow techniques for quantum Markov semigroups","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N"}],"author":[{"full_name":"Keller, Matthias","first_name":"Matthias","last_name":"Keller"},{"first_name":"Daniel","last_name":"Lenz","full_name":"Lenz, Daniel"},{"last_name":"Schmidt","first_name":"Marcel","full_name":"Schmidt, Marcel"},{"first_name":"Michael","last_name":"Schwarz","full_name":"Schwarz, Michael"},{"full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","first_name":"Melchior","orcid":"0000-0002-0519-4241"}],"status":"public","quality_controlled":"1","arxiv":1,"type":"journal_article","oa":1,"date_created":"2025-12-14T23:02:03Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s11118-025-10251-y"}],"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"}]},{"status":"public","quality_controlled":"1","type":"journal_article","file":[{"file_id":"18497","checksum":"143816823b5f43bd3748da8e3e91cef5","file_size":911476,"creator":"dernst","access_level":"open_access","date_updated":"2024-11-04T08:54:26Z","relation":"main_file","success":1,"file_name":"2024_JourLondonMathSoc_Schiavo.pdf","content_type":"application/pdf","date_created":"2024-11-04T08:54:26Z"}],"oa":1,"date_created":"2024-11-03T23:01:44Z","abstract":[{"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. ","lang":"eng"}],"title":"Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension","month":"11","ddc":["510"],"article_type":"original","article_number":"e70003","scopus_import":"1","day":"01","year":"2024","doi":"10.1112/jlms.70003","author":[{"last_name":"Dello Schiavo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"first_name":"Ronan","last_name":"Herry","full_name":"Herry, Ronan"},{"last_name":"Kopfer","first_name":"Eva","full_name":"Kopfer, Eva"},{"first_name":"Karl Theodor","last_name":"Sturm","full_name":"Sturm, Karl Theodor"}],"project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"},{"name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"volume":110,"date_published":"2024-11-01T00:00:00Z","oa_version":"Published Version","ec_funded":1,"publisher":"London Mathematical Society","publication_status":"published","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"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.","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","file_date_updated":"2024-11-04T08:54:26Z","intvolume":" 110","publication":"Journal of the London Mathematical Society","_id":"18490","article_processing_charge":"Yes (via OA deal)","date_updated":"2025-09-08T14:29:45Z","issue":"5","has_accepted_license":"1","OA_type":"hybrid","language":[{"iso":"eng"}],"OA_place":"publisher","department":[{"_id":"JaMa"}],"publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"citation":{"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.","short":"L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Journal of the London Mathematical Society 110 (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. Journal of the London Mathematical Society. 2024;110(5). doi:10.1112/jlms.70003","mla":"Dello Schiavo, Lorenzo, et al. “Conformally Invariant Random Fields, Liouville Quantum Gravity Measures, and Random Paneitz Operators on Riemannian Manifolds of Even Dimension.” Journal of the London Mathematical Society, vol. 110, no. 5, e70003, London Mathematical Society, 2024, doi:10.1112/jlms.70003.","apa":"Dello Schiavo, L., Herry, R., Kopfer, E., & Sturm, K. T. (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. London Mathematical Society. https://doi.org/10.1112/jlms.70003","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,” Journal of the London Mathematical Society, vol. 110, no. 5. London Mathematical Society, 2024.","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.” Journal of the London Mathematical Society. London Mathematical Society, 2024. https://doi.org/10.1112/jlms.70003."},"external_id":{"isi":["001351918100029"]}},{"isi":1,"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.","publication":"Annals of Applied Probability","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","intvolume":" 34","oa_version":"Preprint","ec_funded":1,"date_published":"2024-04-01T00:00:00Z","volume":34,"publisher":"Institute of Mathematical Statistics","publication_status":"published","language":[{"iso":"eng"}],"external_id":{"arxiv":["2112.14196"],"isi":["001198623200016"]},"department":[{"_id":"JaMa"}],"publication_identifier":{"issn":["1050-5164"]},"citation":{"ieee":"L. Dello Schiavo, L. Portinale, and F. Sau, “Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains,” Annals of Applied Probability, vol. 34, no. 2. Institute of Mathematical Statistics, pp. 1789–1845, 2024.","chicago":"Dello Schiavo, Lorenzo, Lorenzo Portinale, and Federico Sau. “Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Nonequilibrium States in Lipschitz Domains.” Annals of Applied Probability. Institute of Mathematical Statistics, 2024. https://doi.org/10.1214/23-AAP2007.","apa":"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. Institute of Mathematical Statistics. https://doi.org/10.1214/23-AAP2007","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.” Annals of Applied Probability, vol. 34, no. 2, Institute of Mathematical Statistics, 2024, pp. 1789–845, doi:10.1214/23-AAP2007.","ama":"Dello Schiavo L, Portinale L, Sau F. Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains. Annals of Applied Probability. 2024;34(2):1789-1845. doi:10.1214/23-AAP2007"},"article_processing_charge":"No","date_updated":"2025-09-04T13:36:00Z","_id":"15317","issue":"2","oa":1,"type":"journal_article","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2112.14196"}],"abstract":[{"lang":"eng","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."}],"date_created":"2024-04-14T22:01:02Z","arxiv":1,"quality_controlled":"1","status":"public","corr_author":"1","article_type":"original","doi":"10.1214/23-AAP2007","year":"2024","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":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo","last_name":"Portinale"},{"first_name":"Federico","last_name":"Sau","id":"E1836206-9F16-11E9-8814-AEFDE5697425","full_name":"Sau, Federico"}],"project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"name":"Reaching consensus in heterogeneous random opinion dynamics","grant_number":"M03211","_id":"3490b268-11ca-11ed-8bc3-e0ad03f48839"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"},{"grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","name":"Configuration Spaces over Non-Smooth Spaces"},{"name":"Dissipation and dispersion in nonlinear partial differential equations","call_identifier":"FWF","grant_number":"W1245","_id":"260788DE-B435-11E9-9278-68D0E5697425"}],"scopus_import":"1","page":"1789-1845","day":"01","month":"04","title":"Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains"},{"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.","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"publication":"Calculus of Variations and Partial Differential Equations","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","file_date_updated":"2024-07-22T07:05:32Z","intvolume":" 63","oa_version":"Published Version","ec_funded":1,"volume":63,"date_published":"2024-07-01T00:00:00Z","publisher":"Springer Nature","publication_status":"published","has_accepted_license":"1","language":[{"iso":"eng"}],"external_id":{"arxiv":["2209.11149"],"isi":["001258097800003"],"pmid":["38947856"]},"department":[{"_id":"JaMa"}],"pmid":1,"citation":{"apa":"Brooks, M., & Maas, J. (2024). Characterisation of gradient flows for a given functional. Calculus of Variations and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-024-02755-z","ama":"Brooks M, Maas J. Characterisation of gradient flows for a given functional. Calculus of Variations and Partial Differential Equations. 2024;63(6). doi:10.1007/s00526-024-02755-z","mla":"Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a given Functional.” Calculus of Variations and Partial Differential Equations, vol. 63, no. 6, 153, Springer Nature, 2024, doi:10.1007/s00526-024-02755-z.","ista":"Brooks M, Maas J. 2024. Characterisation of gradient flows for a given functional. Calculus of Variations and Partial Differential Equations. 63(6), 153.","short":"M. Brooks, J. Maas, Calculus of Variations and Partial Differential Equations 63 (2024).","chicago":"Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a given Functional.” Calculus of Variations and Partial Differential Equations. Springer Nature, 2024. https://doi.org/10.1007/s00526-024-02755-z.","ieee":"M. Brooks and J. Maas, “Characterisation of gradient flows for a given functional,” Calculus of Variations and Partial Differential Equations, vol. 63, no. 6. Springer Nature, 2024."},"publication_identifier":{"eissn":["1432-0835"],"issn":["0944-2669"]},"article_processing_charge":"Yes (via OA deal)","date_updated":"2025-09-08T08:24:51Z","_id":"17282","issue":"6","file":[{"checksum":"a0cf0e0ba2157aabb287cb597be17dac","file_size":416622,"file_id":"17289","relation":"main_file","access_level":"open_access","creator":"dernst","date_updated":"2024-07-22T07:05:32Z","file_name":"2024_CalculusVariations_Brooks.pdf","date_created":"2024-07-22T07:05:32Z","content_type":"application/pdf","success":1}],"oa":1,"type":"journal_article","abstract":[{"lang":"eng","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."}],"date_created":"2024-07-21T22:01:01Z","quality_controlled":"1","arxiv":1,"status":"public","corr_author":"1","article_number":"153","article_type":"original","year":"2024","doi":"10.1007/s00526-024-02755-z","author":[{"id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","full_name":"Brooks, Morris","first_name":"Morris","last_name":"Brooks","orcid":"0000-0002-6249-0928"},{"last_name":"Maas","first_name":"Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan"}],"project":[{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"scopus_import":"1","day":"01","month":"07","title":"Characterisation of gradient flows for a given functional","ddc":["510"]},{"status":"public","corr_author":"1","file":[{"file_id":"17366","checksum":"11650bab714ef85ad43a287060850523","file_size":2941599,"creator":"fpedrott","access_level":"open_access","date_updated":"2024-08-02T09:23:26Z","relation":"main_file","success":1,"file_name":"thesis_final.pdf","content_type":"application/pdf","date_created":"2024-08-02T09:23:26Z"},{"content_type":"application/x-zip-compressed","date_created":"2024-08-02T09:27:15Z","file_name":"thesis_final_source.zip","file_size":6293375,"checksum":"c30ba5611941226cf1bfc867c25b1e80","file_id":"17367","relation":"source_file","date_updated":"2024-08-02T09:27:15Z","access_level":"closed","creator":"fpedrott"}],"oa":1,"type":"dissertation","abstract":[{"lang":"eng","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"}],"date_created":"2024-07-29T09:14:14Z","month":"07","title":"Functional inequalities and convergence of stochastic processes","ddc":["500","510","515","519"],"related_material":{"record":[{"id":"17351","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"17353"},{"id":"17350","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"17352"},{"status":"public","relation":"part_of_dissertation","id":"17143"}]},"degree_awarded":"PhD","year":"2024","doi":"10.15479/at:ista:17336","project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"author":[{"id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","full_name":"Pedrotti, Francesco","last_name":"Pedrotti","first_name":"Francesco"}],"page":"183","day":"31","oa_version":"Published Version","ec_funded":1,"date_published":"2024-07-31T00:00:00Z","publisher":"Institute of Science and Technology Austria","publication_status":"published","supervisor":[{"orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"alternative_title":["ISTA Thesis"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","image":"/images/cc_by_nc_nd.png"},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","file_date_updated":"2024-08-02T09:27:15Z","article_processing_charge":"No","date_updated":"2026-04-07T13:00:03Z","_id":"17336","has_accepted_license":"1","language":[{"iso":"eng"}],"OA_place":"publisher","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"publication_identifier":{"issn":["2663-337X"]},"citation":{"ama":"Pedrotti F. Functional inequalities and convergence of stochastic processes. 2024. doi:10.15479/at:ista:17336","mla":"Pedrotti, Francesco. Functional Inequalities and Convergence of Stochastic Processes. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17336.","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.","apa":"Pedrotti, F. (2024). Functional inequalities and convergence of stochastic processes. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17336","chicago":"Pedrotti, Francesco. “Functional Inequalities and Convergence of Stochastic Processes.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17336.","ieee":"F. Pedrotti, “Functional inequalities and convergence of stochastic processes,” Institute of Science and Technology Austria, 2024."}},{"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","intvolume":" 377","publication":"Transactions of the American Mathematical Society","isi":1,"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","publisher":"American Mathematical Society","publication_status":"published","volume":377,"date_published":"2024-06-01T00:00:00Z","oa_version":"Preprint","ec_funded":1,"department":[{"_id":"JaMa"}],"citation":{"apa":"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. American Mathematical Society. https://doi.org/10.1090/tran/9156","mla":"Dello Schiavo, Lorenzo, et al. “Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces.” Transactions of the American Mathematical Society, vol. 377, no. 6, American Mathematical Society, 2024, pp. 3779–804, doi:10.1090/tran/9156.","ama":"Dello Schiavo L, Maas J, Pedrotti F. Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. Transactions of the American Mathematical Society. 2024;377(6):3779-3804. doi:10.1090/tran/9156","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.","short":"L. Dello Schiavo, J. Maas, F. Pedrotti, Transactions of the American Mathematical Society 377 (2024) 3779–3804.","chicago":"Dello Schiavo, Lorenzo, Jan Maas, and Francesco Pedrotti. “Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces.” Transactions of the American Mathematical Society. American Mathematical Society, 2024. https://doi.org/10.1090/tran/9156.","ieee":"L. Dello Schiavo, J. Maas, and F. Pedrotti, “Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces,” Transactions of the American Mathematical Society, vol. 377, no. 6. American Mathematical Society, pp. 3779–3804, 2024."},"publication_identifier":{"issn":["0002-9947"],"eissn":["1088-6850"]},"external_id":{"arxiv":["2304.05239"],"isi":["001203273300001"]},"language":[{"iso":"eng"}],"issue":"6","_id":"17143","article_processing_charge":"No","date_updated":"2026-04-07T13:00:02Z","date_created":"2024-06-16T22:01:06Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2304.05239","open_access":"1"}],"abstract":[{"lang":"eng","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."}],"type":"journal_article","oa":1,"status":"public","quality_controlled":"1","arxiv":1,"scopus_import":"1","page":"3779-3804","day":"01","year":"2024","doi":"10.1090/tran/9156","author":[{"orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo"},{"orcid":"0000-0002-0845-1338","first_name":"Jan","last_name":"Maas","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","full_name":"Pedrotti, Francesco","last_name":"Pedrotti","first_name":"Francesco"}],"project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"}],"article_type":"original","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"17336"}]},"title":"Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces","month":"06"},{"corr_author":"1","quality_controlled":"1","arxiv":1,"status":"public","abstract":[{"lang":"eng","text":"Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups."}],"date_created":"2022-09-11T22:01:57Z","oa":1,"file":[{"file_size":554871,"checksum":"8c7b185eba5ccd92ef55c120f654222c","file_id":"14051","relation":"main_file","date_updated":"2023-08-14T11:38:28Z","creator":"dernst","access_level":"open_access","content_type":"application/pdf","date_created":"2023-08-14T11:38:28Z","file_name":"2023_AnnalesHenriPoincare_Wirth.pdf","success":1}],"type":"journal_article","ddc":["510"],"month":"03","title":"Curvature-dimension conditions for symmetric quantum Markov semigroups","author":[{"orcid":"0000-0002-0519-4241","last_name":"Wirth","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior"},{"first_name":"Haonan","last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan"}],"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis"},{"call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"doi":"10.1007/s00023-022-01220-x","year":"2023","day":"01","scopus_import":"1","page":"717-750","article_type":"original","publication_status":"published","publisher":"Springer Nature","ec_funded":1,"oa_version":"Published Version","date_published":"2023-03-01T00:00:00Z","volume":24,"publication":"Annales Henri Poincare","file_date_updated":"2023-08-14T11:38:28Z","intvolume":" 24","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"H.Z. is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. M.W. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117) and from the Austrian Science Fund (FWF) through grant number F65. Both authors would like to thank Jan Maas for fruitful discussions and helpful comments. Open access funding provided by Austrian Science Fund (FWF).","isi":1,"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"date_updated":"2025-04-23T08:53:05Z","article_processing_charge":"Yes (via OA deal)","_id":"12087","external_id":{"arxiv":["2105.08303"],"isi":["000837499800002"],"pmid":["36950223"]},"publication_identifier":{"issn":["1424-0637"]},"citation":{"short":"M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.","ista":"Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 24, 717–750.","mla":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” Annales Henri Poincare, vol. 24, Springer Nature, 2023, pp. 717–50, doi:10.1007/s00023-022-01220-x.","ama":"Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 2023;24:717-750. doi:10.1007/s00023-022-01220-x","apa":"Wirth, M., & Zhang, H. (2023). Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-022-01220-x","ieee":"M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum Markov semigroups,” Annales Henri Poincare, vol. 24. Springer Nature, pp. 717–750, 2023.","chicago":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” Annales Henri Poincare. Springer Nature, 2023. https://doi.org/10.1007/s00023-022-01220-x."},"department":[{"_id":"JaMa"}],"pmid":1,"language":[{"iso":"eng"}],"has_accepted_license":"1"},{"external_id":{"pmid":["36597554"],"isi":["000906214600004"]},"department":[{"_id":"JaMa"}],"pmid":1,"citation":{"apa":"Dello Schiavo, L., & Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. Springer Nature. https://doi.org/10.1007/s00028-022-00859-7","short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","mla":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations, vol. 23, no. 1, 9, Springer Nature, 2023, doi:10.1007/s00028-022-00859-7.","ama":"Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 2023;23(1). doi:10.1007/s00028-022-00859-7","ieee":"L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms under order isomorphisms,” Journal of Evolution Equations, vol. 23, no. 1. Springer Nature, 2023.","chicago":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations. Springer Nature, 2023. https://doi.org/10.1007/s00028-022-00859-7."},"publication_identifier":{"eissn":["1424-3202"],"issn":["1424-3199"]},"has_accepted_license":"1","language":[{"iso":"eng"}],"issue":"1","article_processing_charge":"Yes (via OA deal)","date_updated":"2025-04-23T08:45:56Z","_id":"12104","publication":"Journal of Evolution Equations","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2023-01-20T10:45:06Z","intvolume":" 23","isi":1,"acknowledgement":"Research supported by the Austrian Science Fund (FWF) grant F65 at the Institute of Science and Technology Austria and by the European Research Council (ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 156).","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"publisher":"Springer Nature","publication_status":"published","oa_version":"Published Version","ec_funded":1,"volume":23,"date_published":"2023-01-01T00:00:00Z","doi":"10.1007/s00028-022-00859-7","year":"2023","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"},{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N","name":"Gradient flow techniques for quantum Markov semigroups"}],"author":[{"last_name":"Dello Schiavo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo"},{"orcid":"0000-0002-0519-4241","first_name":"Melchior","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior"}],"scopus_import":"1","day":"01","article_number":"9","article_type":"original","ddc":["510"],"month":"01","title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","abstract":[{"lang":"eng","text":"We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces."}],"date_created":"2023-01-08T23:00:53Z","oa":1,"file":[{"file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","content_type":"application/pdf","date_created":"2023-01-20T10:45:06Z","success":1,"checksum":"1f34f3e2cb521033de6154f274ea3a4e","file_size":422612,"file_id":"12325","relation":"main_file","access_level":"open_access","creator":"dernst","date_updated":"2023-01-20T10:45:06Z"}],"type":"journal_article","corr_author":"1","quality_controlled":"1","status":"public"},{"publisher":"Elsevier","publication_status":"published","date_published":"2023-08-15T00:00:00Z","volume":285,"oa_version":"Preprint","ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 285","publication":"Journal of Functional Analysis","isi":1,"acknowledgement":"This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813.","issue":"4","_id":"12911","article_processing_charge":"No","date_updated":"2025-04-15T08:31:52Z","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"citation":{"chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.109963.","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” Journal of Functional Analysis, vol. 285, no. 4. Elsevier, 2023.","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis, vol. 285, no. 4, 109963, Elsevier, 2023, doi:10.1016/j.jfa.2023.109963.","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 2023;285(4). doi:10.1016/j.jfa.2023.109963","short":"D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023).","ista":"Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 285(4), 109963.","apa":"Feliciangeli, D., Gerolin, A., & Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.109963"},"publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"external_id":{"arxiv":["2106.11217"],"isi":["000990804300001"]},"language":[{"iso":"eng"}],"status":"public","arxiv":1,"quality_controlled":"1","date_created":"2023-05-07T22:01:02Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"abstract":[{"lang":"eng","text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem."}],"type":"journal_article","oa":1,"related_material":{"record":[{"id":"9792","relation":"earlier_version","status":"public"}]},"title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","month":"08","scopus_import":"1","day":"15","year":"2023","doi":"10.1016/j.jfa.2023.109963","project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020"},{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","grant_number":"F06504","_id":"260482E2-B435-11E9-9278-68D0E5697425","name":"Taming Complexity in Partial Differential Systems"}],"author":[{"id":"41A639AA-F248-11E8-B48F-1D18A9856A87","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","first_name":"Dario","last_name":"Feliciangeli"},{"last_name":"Gerolin","first_name":"Augusto","full_name":"Gerolin, Augusto"},{"last_name":"Portinale","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","full_name":"Portinale, Lorenzo"}],"article_type":"original","article_number":"109963"},{"status":"public","arxiv":1,"quality_controlled":"1","corr_author":"1","type":"journal_article","oa":1,"file":[{"file_id":"14393","checksum":"359bee38d94b7e0aa73925063cb8884d","file_size":1240995,"creator":"dernst","access_level":"open_access","date_updated":"2023-10-04T11:34:10Z","relation":"main_file","success":1,"file_name":"2023_CalculusEquations_Gladbach.pdf","date_created":"2023-10-04T11:34:10Z","content_type":"application/pdf"}],"date_created":"2023-05-14T22:01:00Z","abstract":[{"text":"This paper deals with the large-scale behaviour of dynamical optimal transport on Zd\r\n-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes the effective behaviour of the discrete problems in terms of a continuous optimal transport problem. The effective energy density can be explicitly expressed in terms of a cell formula, which is a finite-dimensional convex programming problem that depends non-trivially on the local geometry of the discrete graph and the discrete energy density. Our homogenisation result is derived from a Γ\r\n-convergence result for action functionals on curves of measures, which we prove under very mild growth conditions on the energy density. We investigate the cell formula in several cases of interest, including finite-volume discretisations of the Wasserstein distance, where non-trivial limiting behaviour occurs.","lang":"eng"}],"title":"Homogenisation of dynamical optimal transport on periodic graphs","month":"04","ddc":["510"],"article_type":"original","article_number":"143","scopus_import":"1","day":"28","year":"2023","doi":"10.1007/s00526-023-02472-z","project":[{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"Dissipation and dispersion in nonlinear partial differential equations","call_identifier":"FWF","grant_number":"W1245","_id":"260788DE-B435-11E9-9278-68D0E5697425"}],"author":[{"full_name":"Gladbach, Peter","first_name":"Peter","last_name":"Gladbach"},{"full_name":"Kopfer, Eva","first_name":"Eva","last_name":"Kopfer"},{"first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan"},{"first_name":"Lorenzo","last_name":"Portinale","full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"}],"date_published":"2023-04-28T00:00:00Z","volume":62,"oa_version":"Published Version","ec_funded":1,"publisher":"Springer Nature","publication_status":"published","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"isi":1,"acknowledgement":"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). J.M and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—350398276. We thank the anonymous reviewer for the careful reading and for useful suggestions. Open access funding provided by Austrian Science Fund (FWF).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 62","file_date_updated":"2023-10-04T11:34:10Z","publication":"Calculus of Variations and Partial Differential Equations","_id":"12959","article_processing_charge":"Yes (via OA deal)","date_updated":"2025-05-15T10:54:12Z","issue":"5","has_accepted_license":"1","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"pmid":1,"publication_identifier":{"eissn":["1432-0835"],"issn":["0944-2669"]},"citation":{"chicago":"Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” Calculus of Variations and Partial Differential Equations. Springer Nature, 2023. https://doi.org/10.1007/s00526-023-02472-z.","ieee":"P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of dynamical optimal transport on periodic graphs,” Calculus of Variations and Partial Differential Equations, vol. 62, no. 5. Springer Nature, 2023.","apa":"Gladbach, P., Kopfer, E., Maas, J., & Portinale, L. (2023). Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-023-02472-z","mla":"Gladbach, Peter, et al. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” Calculus of Variations and Partial Differential Equations, vol. 62, no. 5, 143, Springer Nature, 2023, doi:10.1007/s00526-023-02472-z.","ama":"Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. 2023;62(5). doi:10.1007/s00526-023-02472-z","short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and Partial Differential Equations 62 (2023).","ista":"Gladbach P, Kopfer E, Maas J, Portinale L. 2023. Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. 62(5), 143."},"external_id":{"isi":["000980588900001"],"arxiv":["2110.15321"],"pmid":["37131846"]}},{"language":[{"iso":"eng"}],"has_accepted_license":"1","external_id":{"arxiv":["2003.01366"],"isi":["000704213400001"]},"publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"citation":{"ieee":"L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals and applications,” Potential Analysis, vol. 58. Springer Nature, pp. 573–615, 2023.","chicago":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis. Springer Nature, 2023. https://doi.org/10.1007/s11118-021-09951-y.","short":"L. Dello Schiavo, Potential Analysis 58 (2023) 573–615.","ista":"Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 58, 573–615.","ama":"Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 2023;58:573-615. doi:10.1007/s11118-021-09951-y","mla":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis, vol. 58, Springer Nature, 2023, pp. 573–615, doi:10.1007/s11118-021-09951-y.","apa":"Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-021-09951-y"},"department":[{"_id":"JaMa"}],"date_updated":"2025-04-14T07:27:46Z","article_processing_charge":"Yes (via OA deal)","_id":"10145","acknowledgement":"The author is grateful to Professors Sergio Albeverio and Andreas Eberle, and to Dr. Kohei Suzuki, for fruitful conversations on the subject of the present work, and for respectively pointing out the references [1, 13], and [3, 20]. Finally, he is especially grateful to an anonymous Reviewer for their very careful reading and their suggestions which improved the readability of the paper.","isi":1,"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"publication":"Potential Analysis","file_date_updated":"2023-10-04T09:18:59Z","intvolume":" 58","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"oa_version":"Published Version","date_published":"2023-03-01T00:00:00Z","volume":58,"publication_status":"published","publisher":"Springer Nature","article_type":"original","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"}],"author":[{"full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870"}],"doi":"10.1007/s11118-021-09951-y","year":"2023","day":"01","scopus_import":"1","page":"573-615","month":"03","title":"Ergodic decomposition of Dirichlet forms via direct integrals and applications","ddc":["510"],"file":[{"success":1,"file_name":"2023_PotentialAnalysis_DelloSchiavo.pdf","content_type":"application/pdf","date_created":"2023-10-04T09:18:59Z","creator":"dernst","access_level":"open_access","date_updated":"2023-10-04T09:18:59Z","relation":"main_file","file_id":"14387","checksum":"625526482be300ca7281c91c30d41725","file_size":806391}],"oa":1,"type":"journal_article","abstract":[{"text":"We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique.","lang":"eng"}],"date_created":"2021-10-17T22:01:17Z","arxiv":1,"quality_controlled":"1","status":"public","corr_author":"1"},{"has_accepted_license":"1","language":[{"iso":"eng"}],"external_id":{"isi":["001021692200001"],"pmid":["37065438"]},"pmid":1,"department":[{"_id":"GradSch"},{"_id":"BeVi"}],"citation":{"apa":"Mrnjavac, A., Khudiakova, K., Barton, N. H., & Vicoso, B. (2023). Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution. Evolution Letters. Oxford University Press. https://doi.org/10.1093/evlett/qrac004","short":"A. Mrnjavac, K. Khudiakova, N.H. Barton, B. Vicoso, Evolution Letters 7 (2023).","ista":"Mrnjavac A, Khudiakova K, Barton NH, Vicoso B. 2023. Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution. Evolution Letters. 7(1), qrac004.","ama":"Mrnjavac A, Khudiakova K, Barton NH, Vicoso B. Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution. Evolution Letters. 2023;7(1). doi:10.1093/evlett/qrac004","mla":"Mrnjavac, Andrea, et al. “Slower-X: Reduced Efficiency of Selection in the Early Stages of X Chromosome Evolution.” Evolution Letters, vol. 7, no. 1, qrac004, Oxford University Press, 2023, doi:10.1093/evlett/qrac004.","ieee":"A. Mrnjavac, K. Khudiakova, N. H. Barton, and B. Vicoso, “Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution,” Evolution Letters, vol. 7, no. 1. Oxford University Press, 2023.","chicago":"Mrnjavac, Andrea, Kseniia Khudiakova, Nicholas H Barton, and Beatriz Vicoso. “Slower-X: Reduced Efficiency of Selection in the Early Stages of X Chromosome Evolution.” Evolution Letters. Oxford University Press, 2023. https://doi.org/10.1093/evlett/qrac004."},"publication_identifier":{"issn":["2056-3744"]},"article_processing_charge":"Yes (via OA deal)","date_updated":"2026-04-30T22:30:24Z","_id":"12521","issue":"1","isi":1,"acknowledgement":"We thank the Vicoso and Barton groups and ISTA Scientific Computing Unit. We also thank two anonymous reviewers for their valuable comments. This work was supported by the European Research Council under the European Union’s Horizon 2020 research and innovation program (grant agreements no. 715257 and no. 716117).","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"publication":"Evolution Letters","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2023-08-16T11:43:33Z","intvolume":" 7","oa_version":"Published Version","ec_funded":1,"volume":7,"date_published":"2023-02-01T00:00:00Z","publisher":"Oxford University Press","publication_status":"published","article_number":"qrac004","article_type":"original","doi":"10.1093/evlett/qrac004","year":"2023","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Prevalence and Influence of Sexual Antagonism on Genome Evolution","call_identifier":"H2020","grant_number":"715257","_id":"250BDE62-B435-11E9-9278-68D0E5697425"}],"author":[{"id":"353FAC84-AE61-11E9-8BFC-00D3E5697425","full_name":"Mrnjavac, Andrea","last_name":"Mrnjavac","first_name":"Andrea"},{"orcid":"0000-0002-6246-1465","first_name":"Kseniia","last_name":"Khudiakova","id":"4E6DC800-AE37-11E9-AC72-31CAE5697425","full_name":"Khudiakova, Kseniia"},{"first_name":"Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Beatriz","last_name":"Vicoso","orcid":"0000-0002-4579-8306","full_name":"Vicoso, Beatriz","id":"49E1C5C6-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","day":"01","month":"02","title":"Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution","ddc":["570"],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"18531"}]},"file":[{"checksum":"a240a041cb9b9b7c8ba93a4706674a3f","file_size":2592189,"file_id":"14068","relation":"main_file","creator":"dernst","access_level":"open_access","date_updated":"2023-08-16T11:43:33Z","file_name":"2023_EvLetters_Mrnjavac.pdf","date_created":"2023-08-16T11:43:33Z","content_type":"application/pdf","success":1}],"oa":1,"keyword":["Genetics","Ecology","Evolution","Behavior and Systematics"],"type":"journal_article","abstract":[{"text":"Differentiated X chromosomes are expected to have higher rates of adaptive divergence than autosomes, if new beneficial mutations are recessive (the “faster-X effect”), largely because these mutations are immediately exposed to selection in males. The evolution of X chromosomes after they stop recombining in males, but before they become hemizygous, has not been well explored theoretically. We use the diffusion approximation to infer substitution rates of beneficial and deleterious mutations under such a scenario. Our results show that selection is less efficient on diploid X loci than on autosomal and hemizygous X loci under a wide range of parameters. This “slower-X” effect is stronger for genes affecting primarily (or only) male fitness, and for sexually antagonistic genes. These unusual dynamics suggest that some of the peculiar features of X chromosomes, such as the differential accumulation of genes with sex-specific functions, may start arising earlier than previously appreciated.","lang":"eng"}],"date_created":"2023-02-06T13:59:12Z","quality_controlled":"1","status":"public","corr_author":"1"},{"publication_identifier":{"eissn":["1556-181X"],"issn":["1556-1801"]},"citation":{"chicago":"Erbar, Matthias, Dominik L Forkert, Jan Maas, and Delio Mugnolo. “Gradient Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric Graph.” Networks and Heterogeneous Media. American Institute of Mathematical Sciences, 2022. https://doi.org/10.3934/nhm.2022023.","ieee":"M. Erbar, D. L. Forkert, J. Maas, and D. Mugnolo, “Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph,” Networks and Heterogeneous Media, vol. 17, no. 5. American Institute of Mathematical Sciences, pp. 687–717, 2022.","apa":"Erbar, M., Forkert, D. L., Maas, J., & Mugnolo, D. (2022). Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media. American Institute of Mathematical Sciences. https://doi.org/10.3934/nhm.2022023","mla":"Erbar, Matthias, et al. “Gradient Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric Graph.” Networks and Heterogeneous Media, vol. 17, no. 5, American Institute of Mathematical Sciences, 2022, pp. 687–717, doi:10.3934/nhm.2022023.","ama":"Erbar M, Forkert DL, Maas J, Mugnolo D. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media. 2022;17(5):687-717. doi:10.3934/nhm.2022023","ista":"Erbar M, Forkert DL, Maas J, Mugnolo D. 2022. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media. 17(5), 687–717.","short":"M. Erbar, D.L. Forkert, J. Maas, D. Mugnolo, Networks and Heterogeneous Media 17 (2022) 687–717."},"department":[{"_id":"JaMa"}],"external_id":{"arxiv":["2105.05677"],"isi":["000812422100001"]},"language":[{"iso":"eng"}],"issue":"5","_id":"11700","date_updated":"2025-04-14T07:27:47Z","article_processing_charge":"No","intvolume":" 17","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication":"Networks and Heterogeneous Media","acknowledgement":"ME acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG), Grant SFB 1283/2 2021 – 317210226. DF and JM were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117). JM also acknowledges support by the Austrian Science Fund (FWF), Project SFB F65. The work of DM was partially supported by the Deutsche Forschungsgemeinschaft\r\n(DFG), Grant 397230547. This article is based upon work from COST Action\r\n18232 MAT-DYN-NET, supported by COST (European Cooperation in Science\r\nand Technology), www.cost.eu. We wish to thank Martin Burger and Jan-Frederik\r\nPietschmann for useful discussions. We are grateful to the anonymous referees for\r\ntheir careful reading and useful suggestions.","isi":1,"publication_status":"published","publisher":"American Institute of Mathematical Sciences","volume":17,"date_published":"2022-10-01T00:00:00Z","ec_funded":1,"oa_version":"Preprint","day":"01","page":"687-717","scopus_import":"1","author":[{"full_name":"Erbar, Matthias","last_name":"Erbar","first_name":"Matthias"},{"first_name":"Dominik L","last_name":"Forkert","full_name":"Forkert, Dominik L","id":"35C79D68-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan"},{"first_name":"Delio","last_name":"Mugnolo","full_name":"Mugnolo, Delio"}],"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"year":"2022","doi":"10.3934/nhm.2022023","article_type":"original","title":"Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph","month":"10","date_created":"2022-07-31T22:01:46Z","abstract":[{"text":"This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou–Brenier formula for the Wasserstein distance, which establishes the equivalence of static and dynamical optimal transport. Secondly, in the spirit of Jordan–Kinderlehrer–Otto, we show that McKean–Vlasov equations can be formulated as gradient flow of the free energy in the Wasserstein space of probability measures. The proofs of these results are based on careful regularisation arguments to circumvent some of the difficulties arising in metric graphs, namely, branching of geodesics and the failure of semi-convexity of entropy functionals in the Wasserstein space.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.05677"}],"type":"journal_article","oa":1,"corr_author":"1","status":"public","quality_controlled":"1","arxiv":1},{"title":"Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions","month":"07","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"10022"}]},"article_type":"original","day":"18","scopus_import":"1","page":"4297-4333","author":[{"id":"35C79D68-F248-11E8-B48F-1D18A9856A87","full_name":"Forkert, Dominik L","first_name":"Dominik L","last_name":"Forkert"},{"full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338"},{"first_name":"Lorenzo","last_name":"Portinale","full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"}],"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"name":"Dissipation and dispersion in nonlinear partial differential equations","_id":"260788DE-B435-11E9-9278-68D0E5697425","grant_number":"W1245","call_identifier":"FWF"}],"year":"2022","doi":"10.1137/21M1410968","status":"public","quality_controlled":"1","arxiv":1,"corr_author":"1","type":"journal_article","keyword":["Fokker--Planck equation","gradient flow","evolutionary $\\Gamma$-convergence"],"oa":1,"date_created":"2022-08-07T22:01:59Z","abstract":[{"text":"We consider finite-volume approximations of Fokker--Planck equations on bounded convex domains in $\\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker--Planck equation via the method of evolutionary $\\Gamma$-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalizing the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2008.10962"}],"_id":"11739","date_updated":"2025-04-15T08:31:31Z","article_processing_charge":"No","issue":"4","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1095-7154"],"issn":["0036-1410"]},"citation":{"chicago":"Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21M1410968.","ieee":"D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” SIAM Journal on Mathematical Analysis, vol. 54, no. 4. Society for Industrial and Applied Mathematics, pp. 4297–4333, 2022.","mla":"Forkert, Dominik L., et al. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” SIAM Journal on Mathematical Analysis, vol. 54, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 4297–333, doi:10.1137/21M1410968.","ama":"Forkert DL, Maas J, Portinale L. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. 2022;54(4):4297-4333. doi:10.1137/21M1410968","short":"D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis 54 (2022) 4297–4333.","ista":"Forkert DL, Maas J, Portinale L. 2022. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. 54(4), 4297–4333.","apa":"Forkert, D. L., Maas, J., & Portinale, L. (2022). Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21M1410968"},"department":[{"_id":"JaMa"}],"external_id":{"arxiv":["2008.10962"],"isi":["000889274600001"]},"volume":54,"date_published":"2022-07-18T00:00:00Z","ec_funded":1,"oa_version":"Preprint","publication_status":"published","publisher":"Society for Industrial and Applied Mathematics","acknowledgement":"This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme grant 716117 and by the AustrianScience Fund (FWF) through grants F65 and W1245.","isi":1,"intvolume":" 54","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication":"SIAM Journal on Mathematical Analysis"},{"publication_status":"published","publisher":"American Mathematical Society","ec_funded":1,"oa_version":"Published Version","date_published":"2022-11-02T00:00:00Z","volume":9,"publication":"Proceedings of the American Mathematical Society, Series B","intvolume":" 9","file_date_updated":"2023-01-26T13:02:07Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"The first author was partially supported by the National Science Foundation under Grant\r\nNo. DMS-1928930 while participating in a program hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2020 semester. The second author gratefully acknowledges funding by the Austrian Science Fund (FWF) through grants F65 and ESPRIT 208, by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas), and by the Deutsche Forschungsgemeinschaft through the SPP 2265.","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","image":"/images/cc_by_nc_nd.png"},"issue":"43","date_updated":"2025-04-14T07:27:48Z","article_processing_charge":"No","_id":"12177","publication_identifier":{"issn":["2330-1511"]},"citation":{"apa":"Cremaschi, T., & Dello Schiavo, L. (2022). Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. American Mathematical Society. https://doi.org/10.1090/bproc/134","ista":"Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 9(43), 445–459.","short":"T. Cremaschi, L. Dello Schiavo, Proceedings of the American Mathematical Society, Series B 9 (2022) 445–459.","mla":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” Proceedings of the American Mathematical Society, Series B, vol. 9, no. 43, American Mathematical Society, 2022, pp. 445–59, doi:10.1090/bproc/134.","ama":"Cremaschi T, Dello Schiavo L. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 2022;9(43):445-459. doi:10.1090/bproc/134","ieee":"T. Cremaschi and L. Dello Schiavo, “Effective contraction of Skinning maps,” Proceedings of the American Mathematical Society, Series B, vol. 9, no. 43. American Mathematical Society, pp. 445–459, 2022.","chicago":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” Proceedings of the American Mathematical Society, Series B. American Mathematical Society, 2022. https://doi.org/10.1090/bproc/134."},"department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"has_accepted_license":"1","corr_author":"1","quality_controlled":"1","status":"public","abstract":[{"lang":"eng","text":"Using elementary hyperbolic geometry, we give an explicit formula for the contraction constant of the skinning map over moduli spaces of relatively acylindrical hyperbolic manifolds."}],"date_created":"2023-01-12T12:12:17Z","oa":1,"file":[{"success":1,"file_name":"2022_ProceedingsAMS_Cremaschi.pdf","date_created":"2023-01-26T13:02:07Z","content_type":"application/pdf","file_id":"12404","checksum":"cb4a79937c1f60d4c329a10ee797f0d2","file_size":326471,"creator":"dernst","access_level":"open_access","date_updated":"2023-01-26T13:02:07Z","relation":"main_file"}],"type":"journal_article","ddc":["510"],"month":"11","title":"Effective contraction of Skinning maps","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"author":[{"full_name":"Cremaschi, Tommaso","first_name":"Tommaso","last_name":"Cremaschi"},{"orcid":"0000-0002-9881-6870","first_name":"Lorenzo","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"}],"year":"2022","doi":"10.1090/bproc/134","day":"02","scopus_import":"1","page":"445-459","article_type":"original"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 384","file_date_updated":"2022-01-03T11:08:31Z","publication":"Mathematische Annalen","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"isi":1,"acknowledgement":"The authors are grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino Antonelli for reading a preliminary version of this work and for their valuable comments and suggestions. Finally, they wish to express their gratitude to two anonymous Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S. gratefully acknowledges funding of his position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium.","publisher":"Springer Nature","publication_status":"published","date_published":"2022-12-01T00:00:00Z","volume":384,"oa_version":"Published Version","ec_funded":1,"department":[{"_id":"JaMa"}],"citation":{"ieee":"L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces and applications,” Mathematische Annalen, vol. 384. Springer Nature, pp. 1815–1832, 2022.","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” Mathematische Annalen. Springer Nature, 2022. https://doi.org/10.1007/s00208-021-02331-2.","ista":"Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 384, 1815–1832.","short":"L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” Mathematische Annalen, vol. 384, Springer Nature, 2022, pp. 1815–32, doi:10.1007/s00208-021-02331-2.","ama":"Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 2022;384:1815-1832. doi:10.1007/s00208-021-02331-2","apa":"Dello Schiavo, L., & Suzuki, K. (2022). Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-021-02331-2"},"publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"external_id":{"arxiv":["2110.05137"],"isi":["000734150200001"]},"has_accepted_license":"1","language":[{"iso":"eng"}],"_id":"10588","article_processing_charge":"Yes (via OA deal)","date_updated":"2025-04-14T07:27:46Z","date_created":"2022-01-02T23:01:35Z","abstract":[{"text":"We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds.","lang":"eng"}],"type":"journal_article","file":[{"date_updated":"2022-01-03T11:08:31Z","access_level":"open_access","creator":"alisjak","relation":"main_file","file_id":"10596","file_size":410090,"checksum":"2593abbf195e38efa93b6006b1e90eb1","success":1,"content_type":"application/pdf","date_created":"2022-01-03T11:08:31Z","file_name":"2021_MathAnn_DelloSchiavo.pdf"}],"oa":1,"keyword":["quasi curvature-dimension condition","sub-riemannian geometry","Sobolev-to-Lipschitz property","Varadhan short-time asymptotics"],"corr_author":"1","status":"public","quality_controlled":"1","arxiv":1,"scopus_import":"1","page":"1815-1832","day":"01","year":"2022","doi":"10.1007/s00208-021-02331-2","project":[{"call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"author":[{"orcid":"0000-0002-9881-6870","first_name":"Lorenzo","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo"},{"last_name":"Suzuki","first_name":"Kohei","full_name":"Suzuki, Kohei"}],"article_type":"original","ddc":["510"],"title":"Sobolev-to-Lipschitz property on QCD- spaces and applications","month":"12"},{"issue":"2","date_updated":"2025-06-12T06:17:37Z","article_processing_charge":"Yes (via OA deal)","_id":"11330","external_id":{"isi":["000780305000001"],"pmid":["35509951"]},"publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"citation":{"chicago":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02911-9.","ieee":"M. Wirth, “A dual formula for the noncommutative transport distance,” Journal of Statistical Physics, vol. 187, no. 2. Springer Nature, 2022.","mla":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” Journal of Statistical Physics, vol. 187, no. 2, 19, Springer Nature, 2022, doi:10.1007/s10955-022-02911-9.","ama":"Wirth M. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 2022;187(2). doi:10.1007/s10955-022-02911-9","ista":"Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19.","short":"M. Wirth, Journal of Statistical Physics 187 (2022).","apa":"Wirth, M. (2022). A dual formula for the noncommutative transport distance. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02911-9"},"department":[{"_id":"JaMa"}],"pmid":1,"language":[{"iso":"eng"}],"has_accepted_license":"1","publication_status":"published","publisher":"Springer Nature","ec_funded":1,"oa_version":"Published Version","date_published":"2022-04-08T00:00:00Z","volume":187,"publication":"Journal of Statistical Physics","file_date_updated":"2022-04-29T11:24:23Z","intvolume":" 187","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"The author wants to thank Jan Maas for helpful comments. He also acknowledges financial support from the Austrian Science Fund (FWF) through Grant Number F65 and from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No. 716117).\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","isi":1,"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"ddc":["510","530"],"month":"04","title":"A dual formula for the noncommutative transport distance","author":[{"full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","first_name":"Melchior","last_name":"Wirth"}],"project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"}],"year":"2022","doi":"10.1007/s10955-022-02911-9","day":"08","scopus_import":"1","article_number":"19","article_type":"original","corr_author":"1","quality_controlled":"1","status":"public","abstract":[{"text":"In this article we study the noncommutative transport distance introduced by Carlen and Maas and its entropic regularization defined by Becker and Li. We prove a duality formula that can be understood as a quantum version of the dual Benamou–Brenier formulation of the Wasserstein distance in terms of subsolutions of a Hamilton–Jacobi–Bellmann equation.","lang":"eng"}],"date_created":"2022-04-24T22:01:43Z","oa":1,"file":[{"file_id":"11338","file_size":362119,"checksum":"f3e0b00884b7dde31347a3756788b473","date_updated":"2022-04-29T11:24:23Z","access_level":"open_access","creator":"dernst","relation":"main_file","success":1,"date_created":"2022-04-29T11:24:23Z","content_type":"application/pdf","file_name":"2022_JourStatisticalPhysics_Wirth.pdf"}],"type":"journal_article"},{"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1811.11598","open_access":"1"}],"abstract":[{"text":"We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.","lang":"eng"}],"date_created":"2022-05-08T22:01:44Z","oa":1,"type":"journal_article","corr_author":"1","arxiv":1,"quality_controlled":"1","status":"public","doi":"10.1214/21-AOP1541","year":"2022","author":[{"first_name":"Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"}],"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","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"}],"scopus_import":"1","page":"591-648","day":"01","article_type":"original","month":"03","title":"The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold","publication":"Annals of Probability","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 50","isi":1,"acknowledgement":"Research supported by the Sonderforschungsbereich 1060 and the Hausdorff Center for Mathematics. The author gratefully acknowledges funding of his current position at IST Austria by the Austrian Science Fund (FWF) grant F65 and by the European Research Council (ERC, Grant agreement No. 716117, awarded to Prof. Dr. Jan Maas).","publisher":"Institute of Mathematical Statistics","publication_status":"published","oa_version":"Preprint","ec_funded":1,"date_published":"2022-03-01T00:00:00Z","volume":50,"external_id":{"arxiv":["1811.11598"],"isi":["000773518500005"]},"department":[{"_id":"JaMa"}],"publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"citation":{"ieee":"L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold,” Annals of Probability, vol. 50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.","chicago":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1541.","ista":"Dello Schiavo L. 2022. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. 50(2), 591–648.","short":"L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.","ama":"Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. 2022;50(2):591-648. doi:10.1214/21-AOP1541","mla":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability, vol. 50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:10.1214/21-AOP1541.","apa":"Dello Schiavo, L. (2022). The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1541"},"language":[{"iso":"eng"}],"issue":"2","article_processing_charge":"No","date_updated":"2025-04-14T07:27:47Z","_id":"11354"}]