[{"external_id":{"arxiv":["2504.08658"]},"department":[{"_id":"JaMa"}],"citation":{"apa":"Brigati, G., Dolbeault, J., &#38; Simonov, N. (2026). Logarithmic Sobolev Inequalities: A review on stability and instability results. <i>La Matematica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s44007-025-00180-y\">https://doi.org/10.1007/s44007-025-00180-y</a>","mla":"Brigati, Giovanni, et al. “Logarithmic Sobolev Inequalities: A Review on Stability and Instability Results.” <i>La Matematica</i>, vol. 5, 5, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s44007-025-00180-y\">10.1007/s44007-025-00180-y</a>.","ama":"Brigati G, Dolbeault J, Simonov N. Logarithmic Sobolev Inequalities: A review on stability and instability results. <i>La Matematica</i>. 2026;5. doi:<a href=\"https://doi.org/10.1007/s44007-025-00180-y\">10.1007/s44007-025-00180-y</a>","ista":"Brigati G, Dolbeault J, Simonov N. 2026. Logarithmic Sobolev Inequalities: A review on stability and instability results. La Matematica. 5, 5.","short":"G. Brigati, J. Dolbeault, N. Simonov, La Matematica 5 (2026).","chicago":"Brigati, Giovanni, Jean Dolbeault, and Nikita Simonov. “Logarithmic Sobolev Inequalities: A Review on Stability and Instability Results.” <i>La Matematica</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s44007-025-00180-y\">https://doi.org/10.1007/s44007-025-00180-y</a>.","ieee":"G. Brigati, J. Dolbeault, and N. Simonov, “Logarithmic Sobolev Inequalities: A review on stability and instability results,” <i>La Matematica</i>, vol. 5. Springer Nature, 2026."},"publication_identifier":{"issn":["2730-9657"]},"has_accepted_license":"1","OA_type":"hybrid","OA_place":"publisher","language":[{"iso":"eng"}],"article_processing_charge":"Yes (via OA deal)","date_updated":"2026-01-21T07:48:28Z","_id":"21018","license":"https://creativecommons.org/licenses/by/4.0/","publication":"La Matematica","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2026-01-21T07:45:03Z","intvolume":"         5","acknowledgement":"This work has been supported by the Project Conviviality (ANR-23-CE40–0003) of the French National Research Agency. G.B. has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. The authors thank a referee for a careful reading and suggestions which result in a significant improvement of the manuscript. Open access funding provided by Institute of Science and Technology (IST Austria). The work of GB has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. This work has been supported by the Project Conviviality (ANR-23-CE40–0003) of the French National Research Agency.","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,"date_published":"2026-01-08T00:00:00Z","volume":5,"doi":"10.1007/s44007-025-00180-y","year":"2026","author":[{"last_name":"Brigati","first_name":"Giovanni","full_name":"Brigati, Giovanni","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1"},{"last_name":"Dolbeault","first_name":"Jean","full_name":"Dolbeault, Jean"},{"full_name":"Simonov, Nikita","last_name":"Simonov","first_name":"Nikita"}],"project":[{"call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program"}],"scopus_import":"1","day":"08","article_number":"5","article_type":"original","PlanS_conform":"1","ddc":["510"],"month":"01","title":"Logarithmic Sobolev Inequalities: A review on stability and instability results","abstract":[{"lang":"eng","text":"In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the Lebesgue and the Gaussian measures, and discuss their differences in terms of moments and stability. We give new and direct proofs, as well as examples and discuss the stability of a logarithmic uncertainty principle. Although we do not cover all aspects of the topic, we hope to contribute to establishing the state of the art."}],"date_created":"2026-01-20T10:14:55Z","file":[{"creator":"dernst","access_level":"open_access","date_updated":"2026-01-21T07:45:03Z","relation":"main_file","file_id":"21025","checksum":"0702d8397f216555b1d5286e5d77f09c","file_size":4992025,"success":1,"file_name":"2026_LaMatematica_Brigati.pdf","date_created":"2026-01-21T07:45:03Z","content_type":"application/pdf"}],"oa":1,"type":"journal_article","corr_author":"1","quality_controlled":"1","arxiv":1,"status":"public"},{"oa_version":"Preprint","ec_funded":1,"date_published":"2026-02-01T00:00:00Z","volume":20,"publisher":"American Institute of Mathematical Sciences","publication_status":"epub_ahead","acknowledgement":"We would like to thank Andreas Eberle and Gabriel Stoltz for many helpful discussions. GB\r\nhas received funding from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101034413. FL wurde gefördert durch die Deutsche Forschungsgemeinschaft (DFG) im Rahmen der Exzellenzstrategie des Bundes und der Länder – GZ2047/1, Projekt-ID 390685813. LW is supported by the National Science Foundation via grant DMS-2407166. He is also indebted to the Mathematical Sciences department at Carnegie Mellon University for partly supporting his visit to Europe in July 2024. Part of this work was completed when GB and LW were visiting the Institute for Applied Mathematics in Bonn. GB and LW would like to thank IAM for their hospitality.","publication":"Kinetic and Related Models","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        20","article_processing_charge":"No","date_updated":"2026-02-16T10:02:47Z","_id":"21132","language":[{"iso":"eng"}],"OA_type":"green","OA_place":"repository","external_id":{"arxiv":["2412.10890"]},"department":[{"_id":"JaMa"}],"publication_identifier":{"issn":["1937-5093"],"eissn":["1937-5077"]},"citation":{"ieee":"G. Brigati, F. Lörler, and L. Wang, “Hypocoercivity meets lifts,” <i>Kinetic and Related Models</i>, vol. 20. American Institute of Mathematical Sciences, pp. 34–55, 2026.","chicago":"Brigati, Giovanni, Francis Lörler, and Lihan Wang. “Hypocoercivity Meets Lifts.” <i>Kinetic and Related Models</i>. American Institute of Mathematical Sciences, 2026. <a href=\"https://doi.org/10.3934/krm.2025020\">https://doi.org/10.3934/krm.2025020</a>.","ista":"Brigati G, Lörler F, Wang L. 2026. Hypocoercivity meets lifts. Kinetic and Related Models. 20, 34–55.","short":"G. Brigati, F. Lörler, L. Wang, Kinetic and Related Models 20 (2026) 34–55.","mla":"Brigati, Giovanni, et al. “Hypocoercivity Meets Lifts.” <i>Kinetic and Related Models</i>, vol. 20, American Institute of Mathematical Sciences, 2026, pp. 34–55, doi:<a href=\"https://doi.org/10.3934/krm.2025020\">10.3934/krm.2025020</a>.","ama":"Brigati G, Lörler F, Wang L. Hypocoercivity meets lifts. <i>Kinetic and Related Models</i>. 2026;20:34-55. doi:<a href=\"https://doi.org/10.3934/krm.2025020\">10.3934/krm.2025020</a>","apa":"Brigati, G., Lörler, F., &#38; Wang, L. (2026). Hypocoercivity meets lifts. <i>Kinetic and Related Models</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/krm.2025020\">https://doi.org/10.3934/krm.2025020</a>"},"quality_controlled":"1","arxiv":1,"status":"public","oa":1,"type":"journal_article","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2412.10890","open_access":"1"}],"abstract":[{"lang":"eng","text":"We unify the variational hypocoercivity framework established by D. Albritton, S. Armstrong, J.-C. Mourrat, and M. Novack [2], with the notion of second-order lifts of reversible diffusion processes, recently introduced by A. Eberle and the second author [30]. We give an abstract, yet fully constructive, presentation of the theory, so that it can be applied to a large class of linear kinetic equations. As this hypocoercivity technique does not twist the reference norm, we can recover accurate and sharp convergence rates in various models. Among those, adaptive Langevin dynamics (ALD) is discussed in full detail and we show that for near-quadratic potentials, with suitable choices of parameters, it is a near-optimal second-order lift of the overdamped Langevin dynamics. As a further consequence, we observe that the Generalised Langevin Equation (GLE) is also a second-order lift, as the standard (kinetic) Langevin dynamics are, of the overdamped Langevin dynamics. Then, convergence of (GLE) cannot exceed ballistic speed, i.e. the square root of the rate of the overdamped regime. We illustrate this phenomenon with explicit computations in a benchmark Gaussian case."}],"date_created":"2026-02-01T23:01:43Z","month":"02","title":"Hypocoercivity meets lifts","article_type":"original","year":"2026","doi":"10.3934/krm.2025020","author":[{"id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","full_name":"Brigati, Giovanni","last_name":"Brigati","first_name":"Giovanni"},{"full_name":"Lörler, Francis","last_name":"Lörler","first_name":"Francis"},{"full_name":"Wang, Lihan","last_name":"Wang","first_name":"Lihan"}],"project":[{"grant_number":"101034413","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program"}],"scopus_import":"1","page":"34-55","day":"01"},{"date_published":"2026-03-14T00:00:00Z","oa_version":"Preprint","ec_funded":1,"publisher":"World Scientific Publishing","publication_status":"epub_ahead","acknowledgement":"This work has been written within the activities of GNCS and GNFM groups of INdAM (Italian\r\nNational Institute of High Mathematics). G.B. has been funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101034413. P.G. has been funded by the European Union - NextGenerationEU, in the framework of the GRINSGrowing Resilient, INclusive and Sustainable (GRINS PE00000018).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Mathematical Models and Methods in Applied Sciences","_id":"21504","article_processing_charge":"No","date_updated":"2026-03-30T06:56:35Z","language":[{"iso":"eng"}],"OA_place":"repository","OA_type":"green","department":[{"_id":"JaMa"}],"publication_identifier":{"issn":["0218-2025"],"eissn":["1793-6314"]},"citation":{"chicago":"Auricchio, Gennaro, Giovanni Brigati, Paolo Giudici, and Giuseppe Toscani. “From Kinetic Theory to AI: A Rediscovery of High-Dimensional Divergences and Their Properties.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2026. <a href=\"https://doi.org/10.1142/S0218202526410010\">https://doi.org/10.1142/S0218202526410010</a>.","ieee":"G. Auricchio, G. Brigati, P. Giudici, and G. Toscani, “From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties,” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2026.","apa":"Auricchio, G., Brigati, G., Giudici, P., &#38; Toscani, G. (2026). From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218202526410010\">https://doi.org/10.1142/S0218202526410010</a>","ama":"Auricchio G, Brigati G, Giudici P, Toscani G. From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties. <i>Mathematical Models and Methods in Applied Sciences</i>. 2026. doi:<a href=\"https://doi.org/10.1142/S0218202526410010\">10.1142/S0218202526410010</a>","mla":"Auricchio, Gennaro, et al. “From Kinetic Theory to AI: A Rediscovery of High-Dimensional Divergences and Their Properties.” <i>Mathematical Models and Methods in Applied Sciences</i>, World Scientific Publishing, 2026, doi:<a href=\"https://doi.org/10.1142/S0218202526410010\">10.1142/S0218202526410010</a>.","ista":"Auricchio G, Brigati G, Giudici P, Toscani G. 2026. From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties. Mathematical Models and Methods in Applied Sciences.","short":"G. Auricchio, G. Brigati, P. Giudici, G. Toscani, Mathematical Models and Methods in Applied Sciences (2026)."},"external_id":{"arxiv":["2507.11387"]},"status":"public","quality_controlled":"1","arxiv":1,"type":"journal_article","oa":1,"date_created":"2026-03-29T22:07:08Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2507.11387"}],"abstract":[{"text":"Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback–Leibler (KL) divergence, originally introduced in kinetic theory as a measure of relative entropy between probability distributions. Just as in machine learning, the ability to quantify the proximity of probability distributions plays a central role in kinetic theory. In this paper, we present a comparative review of divergence measures rooted in kinetic theory, highlighting their theoretical foundations and exploring their potential applications in machine learning and artificial intelligence.","lang":"eng"}],"title":"From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties","month":"03","article_type":"original","scopus_import":"1","day":"14","year":"2026","doi":"10.1142/S0218202526410010","author":[{"full_name":"Auricchio, Gennaro","first_name":"Gennaro","last_name":"Auricchio"},{"first_name":"Giovanni","last_name":"Brigati","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","full_name":"Brigati, Giovanni"},{"last_name":"Giudici","first_name":"Paolo","full_name":"Giudici, Paolo"},{"full_name":"Toscani, Giuseppe","last_name":"Toscani","first_name":"Giuseppe"}],"project":[{"name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413"}]},{"external_id":{"arxiv":["2403.07803"]},"department":[{"_id":"JaMa"}],"citation":{"ieee":"F. Quattrocchi, “Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 65, no. 1. Springer Nature, 2026.","chicago":"Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation with General Dirichlet Boundary Conditions.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00526-025-03193-1\">https://doi.org/10.1007/s00526-025-03193-1</a>.","apa":"Quattrocchi, F. (2026). Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions. <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00526-025-03193-1\">https://doi.org/10.1007/s00526-025-03193-1</a>","ista":"Quattrocchi F. 2026. Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions. Calculus of Variations and Partial Differential Equations. 65(1), 23.","short":"F. Quattrocchi, Calculus of Variations and Partial Differential Equations 65 (2026).","mla":"Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation with General Dirichlet Boundary Conditions.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 65, no. 1, 23, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s00526-025-03193-1\">10.1007/s00526-025-03193-1</a>.","ama":"Quattrocchi F. Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions. <i>Calculus of Variations and Partial Differential Equations</i>. 2026;65(1). doi:<a href=\"https://doi.org/10.1007/s00526-025-03193-1\">10.1007/s00526-025-03193-1</a>"},"publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"has_accepted_license":"1","OA_type":"hybrid","OA_place":"publisher","language":[{"iso":"eng"}],"issue":"1","article_processing_charge":"Yes (via OA deal)","date_updated":"2026-04-07T08:37:46Z","_id":"20865","publication":"Calculus of Variations and Partial Differential Equations","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","intvolume":"        65","file_date_updated":"2026-01-05T12:36:39Z","acknowledgement":"The author would like to thank Jan Maas for suggesting this project and for many helpful comments, Antonio Agresti, Lorenzo Dello Schiavo and Julian Fischer for several fruitful discussions, Oliver Tse for pointing out the reference [10], and the anonymous reviewer for carefully reading this manuscript and providing valuable suggestions. He also gratefully acknowledges support from the Austrian Science Fund (FWF) project 10.55776/F65.Open access funding provided by Institute of Science and Technology (IST Austria).","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","date_published":"2026-01-01T00:00:00Z","volume":65,"doi":"10.1007/s00526-025-03193-1","year":"2026","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"author":[{"full_name":"Quattrocchi, Filippo","id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308","first_name":"Filippo","last_name":"Quattrocchi","orcid":"0009-0000-9773-1931"}],"scopus_import":"1","day":"01","article_number":"23","article_type":"original","PlanS_conform":"1","ddc":["510"],"related_material":{"record":[{"id":"20571","relation":"earlier_version","status":"public"}]},"month":"01","title":"Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions","abstract":[{"text":"We prove the convergence of a modified Jordan–Kinderlehrer–Otto scheme to a solution\r\nto the Fokker–Planck equation in Ω e R^d with general—strictly positive and temporally\r\nconstant—Dirichlet boundary conditions. We work under mild assumptions on the domain,\r\nthe drift, and the initial datum. In the special case where Ω is an interval in R1, we prove\r\nthat such a solution is a gradient flow—curve of maximal slope—within a suitable space of\r\nmeasures, endowed with a modified Wasserstein distance. Our discrete scheme and modified\r\ndistance draw inspiration from contributions by A. Figalli and N. Gigli [J. Math. Pures\r\nAppl. 94, (2010), pp. 107–130], and J. Morales [J. Math. Pures Appl. 112, (2018), pp. 41–88]\r\non an optimal-transport approach to evolution equations with Dirichlet boundary conditions.\r\nSimilarly to these works, we allow the mass to flow from/to the boundary ∂Ω throughout\r\nthe evolution. However, our leading idea is to also keep track of the mass at the boundary\r\nby working with measures defined on the whole closure Ω . The driving functional is a\r\nmodification of the classical relative entropy that also makes use of the information at the\r\nboundary. As an intermediate result, when Ω is an interval in R1, we find a formula for the\r\ndescending slope of this geodesically nonconvex functional.","lang":"eng"}],"date_created":"2025-12-29T12:06:26Z","file":[{"file_name":"2026_CalculusVariations_Quattrocchi.pdf","content_type":"application/pdf","date_created":"2026-01-05T12:36:39Z","success":1,"checksum":"635370d64abaf444f50f5cca60bba1be","file_size":958382,"file_id":"20945","relation":"main_file","creator":"dernst","access_level":"open_access","date_updated":"2026-01-05T12:36:39Z"}],"oa":1,"type":"journal_article","corr_author":"1","arxiv":1,"quality_controlled":"1","status":"public"},{"title":"Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous","month":"01","ddc":["510"],"article_type":"original","day":"01","scopus_import":"1","page":"244-281","project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"}],"author":[{"full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","last_name":"Dello Schiavo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870"},{"last_name":"Herry","first_name":"Ronan","full_name":"Herry, Ronan"},{"first_name":"Eva","last_name":"Kopfer","full_name":"Kopfer, Eva"},{"first_name":"Karl Theodor","last_name":"Sturm","full_name":"Sturm, Karl Theodor"}],"year":"2025","doi":"10.1002/mana.202400169","status":"public","quality_controlled":"1","arxiv":1,"type":"journal_article","oa":1,"file":[{"file_name":"2025_MathNachrichten_DelloSchiavo.pdf","content_type":"application/pdf","date_created":"2025-01-13T10:34:42Z","success":1,"relation":"main_file","access_level":"open_access","creator":"dernst","date_updated":"2025-01-13T10:34:42Z","checksum":"1dc50d156feb777c86d779fb1c9ac875","file_size":1734511,"file_id":"18838"}],"date_created":"2024-12-08T23:01:56Z","abstract":[{"text":"For an arbitrary dimension (Formula presented.), we study: the polyharmonic Gaussian field (Formula presented.) on the discrete torus (Formula presented.), that is the random field whose law on (Formula presented.) given by (Formula presented.) where (Formula presented.) is the Lebesgue measure and (Formula presented.) is the discrete Laplacian; the associated discrete Liouville quantum gravity (LQG) measure associated with it, that is, the random measure on (Formula presented.) (Formula presented.) where (Formula presented.) is a regularity parameter. As (Formula presented.), we prove convergence of the fields (Formula presented.) to the polyharmonic Gaussian field (Formula presented.) on the continuous torus (Formula presented.), as well as convergence of the random measures (Formula presented.) to the LQG measure (Formula presented.) on (Formula presented.), for all (Formula presented.). ","lang":"eng"}],"_id":"18632","date_updated":"2025-04-14T07:27:49Z","article_processing_charge":"Yes (via OA deal)","issue":"1","OA_place":"publisher","OA_type":"hybrid","language":[{"iso":"eng"}],"has_accepted_license":"1","publication_identifier":{"eissn":["1522-2616"],"issn":["0025-584X"]},"citation":{"apa":"Dello Schiavo, L., Herry, R., Kopfer, E., &#38; Sturm, K. T. (2025). Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous. <i>Mathematische Nachrichten</i>. Wiley. <a href=\"https://doi.org/10.1002/mana.202400169\">https://doi.org/10.1002/mana.202400169</a>","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.","ama":"Dello Schiavo L, Herry R, Kopfer E, Sturm KT. Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous. <i>Mathematische Nachrichten</i>. 2025;298(1):244-281. doi:<a href=\"https://doi.org/10.1002/mana.202400169\">10.1002/mana.202400169</a>","mla":"Dello Schiavo, Lorenzo, et al. “Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary Dimension: From Discrete to Continuous.” <i>Mathematische Nachrichten</i>, vol. 298, no. 1, Wiley, 2025, pp. 244–81, doi:<a href=\"https://doi.org/10.1002/mana.202400169\">10.1002/mana.202400169</a>.","ieee":"L. Dello Schiavo, R. Herry, E. Kopfer, and K. T. Sturm, “Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous,” <i>Mathematische Nachrichten</i>, vol. 298, no. 1. Wiley, pp. 244–281, 2025.","chicago":"Dello Schiavo, Lorenzo, Ronan Herry, Eva Kopfer, and Karl Theodor Sturm. “Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary Dimension: From Discrete to Continuous.” <i>Mathematische Nachrichten</i>. Wiley, 2025. <a href=\"https://doi.org/10.1002/mana.202400169\">https://doi.org/10.1002/mana.202400169</a>."},"department":[{"_id":"JaMa"}],"external_id":{"arxiv":["2302.02963"],"isi":["001366948500001"]},"date_published":"2025-01-01T00:00:00Z","volume":298,"ec_funded":1,"oa_version":"Published Version","publication_status":"published","publisher":"Wiley","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":"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.","isi":1,"file_date_updated":"2025-01-13T10:34:42Z","intvolume":"       298","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Mathematische Nachrichten"},{"article_type":"original","page":"196 - 250","scopus_import":"1","day":"01","year":"2025","doi":"10.1214/24-aap2113","author":[{"id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","full_name":"Pedrotti, Francesco","first_name":"Francesco","last_name":"Pedrotti"}],"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"}],"title":"Contractive coupling rates and curvature lower bounds for Markov chains","month":"02","related_material":{"record":[{"id":"17351","relation":"earlier_version","status":"public"}]},"type":"journal_article","oa":1,"date_created":"2025-07-21T07:49:15Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2308.00516"}],"abstract":[{"lang":"eng","text":"Contractive coupling rates have been recently introduced by Conforti as a tool to establish convex Sobolev inequalities (including modified log-Sobolev and Poincaré inequality) for some classes of Markov chains. In this work, for most of the examples discussed by Conforti, we use contractive coupling rates to prove stronger inequalities, in the form of curvature lower bounds (in entropic and discrete Bakry–Émery sense) and geodesic convexity of some entropic functionals. In addition, we recall and give straightforward generalizations of some notions of coarse Ricci curvature, and we discuss some of their properties and relations with the concepts of couplings and coupling rates: as an application, we show exponential contraction of the p-Wasserstein distance for the heat flow in the aforementioned examples."}],"status":"public","arxiv":1,"quality_controlled":"1","corr_author":"1","OA_type":"green","OA_place":"repository","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"publication_identifier":{"issn":["1050-5164"]},"citation":{"chicago":"Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/24-aap2113\">https://doi.org/10.1214/24-aap2113</a>.","ieee":"F. Pedrotti, “Contractive coupling rates and curvature lower bounds for Markov chains,” <i>The Annals of Applied Probability</i>, vol. 35, no. 1. Institute of Mathematical Statistics, pp. 196–250, 2025.","apa":"Pedrotti, F. (2025). Contractive coupling rates and curvature lower bounds for Markov chains. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/24-aap2113\">https://doi.org/10.1214/24-aap2113</a>","mla":"Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” <i>The Annals of Applied Probability</i>, vol. 35, no. 1, Institute of Mathematical Statistics, 2025, pp. 196–250, doi:<a href=\"https://doi.org/10.1214/24-aap2113\">10.1214/24-aap2113</a>.","ama":"Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. <i>The Annals of Applied Probability</i>. 2025;35(1):196-250. doi:<a href=\"https://doi.org/10.1214/24-aap2113\">10.1214/24-aap2113</a>","short":"F. Pedrotti, The Annals of Applied Probability 35 (2025) 196–250.","ista":"Pedrotti F. 2025. Contractive coupling rates and curvature lower bounds for Markov chains. The Annals of Applied Probability. 35(1), 196–250."},"external_id":{"isi":["001434322900006"],"arxiv":["2308.00516"]},"_id":"20040","article_processing_charge":"No","date_updated":"2025-11-05T13:50:07Z","issue":"1","isi":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.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        35","publication":"The Annals of Applied Probability","volume":35,"date_published":"2025-02-01T00:00:00Z","oa_version":"Preprint","ec_funded":1,"publisher":"Institute of Mathematical Statistics","publication_status":"published"},{"issue":"3","date_updated":"2025-09-30T14:12:48Z","article_processing_charge":"No","_id":"20050","external_id":{"isi":["001523520000012"],"arxiv":["2402.04151"]},"publication_identifier":{"issn":["1050-5164"]},"citation":{"apa":"Khudiakova, K., Maas, J., &#38; Pedrotti, F. (2025). L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/25-aap2162\">https://doi.org/10.1214/25-aap2162</a>","mla":"Khudiakova, Kseniia, et al. “L∞-Optimal Transport of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” <i>The Annals of Applied Probability</i>, vol. 35, no. 3, Institute of Mathematical Statistics, 2025, pp. 1913–40, doi:<a href=\"https://doi.org/10.1214/25-aap2162\">10.1214/25-aap2162</a>.","ama":"Khudiakova K, Maas J, Pedrotti F. L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. <i>The Annals of Applied Probability</i>. 2025;35(3):1913-1940. doi:<a href=\"https://doi.org/10.1214/25-aap2162\">10.1214/25-aap2162</a>","ista":"Khudiakova K, Maas J, Pedrotti F. 2025. L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. The Annals of Applied Probability. 35(3), 1913–1940.","short":"K. Khudiakova, J. Maas, F. Pedrotti, The Annals of Applied Probability 35 (2025) 1913–1940.","chicago":"Khudiakova, Kseniia, Jan Maas, and Francesco Pedrotti. “L∞-Optimal Transport of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/25-aap2162\">https://doi.org/10.1214/25-aap2162</a>.","ieee":"K. Khudiakova, J. Maas, and F. Pedrotti, “L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model,” <i>The Annals of Applied Probability</i>, vol. 35, no. 3. Institute of Mathematical Statistics, pp. 1913–1940, 2025."},"department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"OA_place":"repository","OA_type":"green","publication_status":"published","publisher":"Institute of Mathematical Statistics","oa_version":"Preprint","volume":35,"date_published":"2025-06-01T00:00:00Z","publication":"The Annals of Applied Probability","intvolume":"        35","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","acknowledgement":"This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/F65 and the Austrian Academy of Science, DOC fellowship nr. 26293.","isi":1,"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"17352"}]},"month":"06","title":"L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model","author":[{"id":"4E6DC800-AE37-11E9-AC72-31CAE5697425","full_name":"Khudiakova, Kseniia","orcid":"0000-0002-6246-1465","first_name":"Kseniia","last_name":"Khudiakova"},{"last_name":"Maas","first_name":"Jan","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pedrotti","first_name":"Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","full_name":"Pedrotti, Francesco"}],"project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"The impact of deleterious mutations on small populations","grant_number":"26293","_id":"34d33d68-11ca-11ed-8bc3-ec13763c0ca8"}],"year":"2025","doi":"10.1214/25-aap2162","day":"01","scopus_import":"1","page":"1913-1940","article_type":"original","corr_author":"1","quality_controlled":"1","arxiv":1,"status":"public","abstract":[{"lang":"eng","text":"We prove upper bounds on the L∞-Wasserstein distance from optimal transport between strongly log-concave probability densities and log-Lipschitz perturbations. In the simplest setting, such a bound amounts to a transport-information inequality involving the L∞-Wasserstein metric and the relative L∞-Fisher information. We show that this inequality can be sharpened significantly in situations where the involved densities are anisotropic. Our proof is based on probabilistic techniques using Langevin dynamics. As an application of these results, we obtain sharp exponential rates of convergence in Fisher’s infinitesimal model from quantitative genetics, generalising recent results by Calvez, Poyato, and Santambrogio in dimension 1 to arbitrary dimensions."}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2402.04151"}],"date_created":"2025-07-21T08:13:54Z","oa":1,"type":"journal_article"},{"publication":"SIAM Journal on Mathematical Analysis","intvolume":"        57","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"The first author was funded by the European Union's Horizon 2020 research andinnovation program under the Marie Sklodowska-Curie grant agreements 754362 and 101034413,and partially by Project EFI (ANR-17-CE40-0030) of the French National Research Agency (ANR).The work of the second author was partially funded by the European Research Council (ERC) underthe European Union's Horizon 2020 research and innovation programme (grant agreement 810367),and by the Agence Nationale de la Recherche under grants ANR-19-CE40-0010 (QuAMProcs) andANR-21-CE40-0006 (SINEQ).","isi":1,"publication_status":"published","publisher":"Society for Industrial and Applied Mathematics","ec_funded":1,"oa_version":"Preprint","volume":57,"date_published":"2025-08-01T00:00:00Z","external_id":{"arxiv":["2302.14506"],"isi":["001550830900006"]},"publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"citation":{"chicago":"Brigati, Giovanni, and Gabriel Stoltz. “How to Construct Explicit Decay Rates for Kinetic Fokker–Planck Equations?” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2025. <a href=\"https://doi.org/10.1137/24M1700351\">https://doi.org/10.1137/24M1700351</a>.","ieee":"G. Brigati and G. Stoltz, “How to construct explicit decay rates for kinetic Fokker–Planck equations?,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 57, no. 4. Society for Industrial and Applied Mathematics, pp. 3587–3622, 2025.","mla":"Brigati, Giovanni, and Gabriel Stoltz. “How to Construct Explicit Decay Rates for Kinetic Fokker–Planck Equations?” <i>SIAM Journal on Mathematical Analysis</i>, vol. 57, no. 4, Society for Industrial and Applied Mathematics, 2025, pp. 3587–622, doi:<a href=\"https://doi.org/10.1137/24M1700351\">10.1137/24M1700351</a>.","ama":"Brigati G, Stoltz G. How to construct explicit decay rates for kinetic Fokker–Planck equations? <i>SIAM Journal on Mathematical Analysis</i>. 2025;57(4):3587-3622. doi:<a href=\"https://doi.org/10.1137/24M1700351\">10.1137/24M1700351</a>","short":"G. Brigati, G. Stoltz, SIAM Journal on Mathematical Analysis 57 (2025) 3587–3622.","ista":"Brigati G, Stoltz G. 2025. How to construct explicit decay rates for kinetic Fokker–Planck equations? SIAM Journal on Mathematical Analysis. 57(4), 3587–3622.","apa":"Brigati, G., &#38; Stoltz, G. (2025). How to construct explicit decay rates for kinetic Fokker–Planck equations? <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/24M1700351\">https://doi.org/10.1137/24M1700351</a>"},"department":[{"_id":"JaMa"}],"OA_type":"green","OA_place":"repository","language":[{"iso":"eng"}],"issue":"4","date_updated":"2025-11-05T13:51:40Z","article_processing_charge":"No","_id":"20155","abstract":[{"lang":"eng","text":"We study time averages for the norm of solutions to kinetic Fokker–Planck equations associated with general Hamiltonians. We provide fully explicit and constructive decay estimates for systems subject to a confining potential, allowing fat-tail, subexponential and (super-)exponential local equilibria, which also include the classic Maxwellian case. The key step in our estimates is a modified Poincaré inequality, obtained via a Lions–Poincaré inequality and an averaging lemma."}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2302.14506","open_access":"1"}],"date_created":"2025-08-10T22:01:29Z","oa":1,"type":"journal_article","corr_author":"1","arxiv":1,"quality_controlled":"1","status":"public","author":[{"id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","full_name":"Brigati, Giovanni","first_name":"Giovanni","last_name":"Brigati"},{"full_name":"Stoltz, Gabriel","first_name":"Gabriel","last_name":"Stoltz"}],"project":[{"grant_number":"101034413","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program"}],"doi":"10.1137/24M1700351","year":"2025","day":"01","scopus_import":"1","page":"3587-3622","article_type":"original","month":"08","title":"How to construct explicit decay rates for kinetic Fokker–Planck equations?"},{"oa_version":"Published Version","ec_funded":1,"volume":30,"date_published":"2025-09-25T00:00:00Z","publisher":"Institute of Mathematical Statistics","publication_status":"published","isi":1,"acknowledgement":"This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/F65 and by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101034413. The authors thank Professors Jean Dolbeault, Jan Maas, and Nikita Simonov for many useful comments, and Professors Kazuhiro Ishige, Asuka Takatsu, and Yair Shenfeld for inspiring interactions.","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":"Electronic Communications in Probability","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2025-11-04T07:34:05Z","intvolume":"        30","article_processing_charge":"Yes","date_updated":"2025-12-01T15:08:54Z","_id":"20591","has_accepted_license":"1","language":[{"iso":"eng"}],"OA_place":"publisher","OA_type":"gold","external_id":{"arxiv":["2404.15205"],"isi":["001611557000018"]},"department":[{"_id":"JaMa"}],"publication_identifier":{"eissn":["1083-589X"]},"citation":{"ama":"Brigati G, Pedrotti F. Heat flow, log-concavity, and Lipschitz transport maps. <i>Electronic Communications in Probability</i>. 2025;30. doi:<a href=\"https://doi.org/10.1214/25-ECP717\">10.1214/25-ECP717</a>","mla":"Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” <i>Electronic Communications in Probability</i>, vol. 30, 71, Institute of Mathematical Statistics, 2025, doi:<a href=\"https://doi.org/10.1214/25-ECP717\">10.1214/25-ECP717</a>.","short":"G. Brigati, F. Pedrotti, Electronic Communications in Probability 30 (2025).","ista":"Brigati G, Pedrotti F. 2025. Heat flow, log-concavity, and Lipschitz transport maps. Electronic Communications in Probability. 30, 71.","apa":"Brigati, G., &#38; Pedrotti, F. (2025). Heat flow, log-concavity, and Lipschitz transport maps. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/25-ECP717\">https://doi.org/10.1214/25-ECP717</a>","chicago":"Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/25-ECP717\">https://doi.org/10.1214/25-ECP717</a>.","ieee":"G. Brigati and F. Pedrotti, “Heat flow, log-concavity, and Lipschitz transport maps,” <i>Electronic Communications in Probability</i>, vol. 30. Institute of Mathematical Statistics, 2025."},"quality_controlled":"1","arxiv":1,"status":"public","corr_author":"1","oa":1,"file":[{"content_type":"application/pdf","date_created":"2025-11-04T07:34:05Z","file_name":"2025_ElectronJourProbab_Brigati.pdf","success":1,"file_size":278078,"checksum":"67858edbd74658fe38955fa1216f2f18","file_id":"20596","relation":"main_file","date_updated":"2025-11-04T07:34:05Z","access_level":"open_access","creator":"dernst"}],"type":"journal_article","abstract":[{"text":"In this paper we derive estimates for the Hessian of the logarithm (log-Hessian) for solutions to the heat equation. For initial data in the form of log-Lipschitz perturbation of strongly log-concave measures, the log-Hessian admits an explicit, uniform (in space) lower bound. This yields a new estimate for the Lipschitz constant of a transport map pushing forward the standard Gaussian to a measure in this class. On the other hand, we show that assuming only fast decay of the tails of the initial datum does not suffice to guarantee uniform log-Hessian upper bounds.","lang":"eng"}],"date_created":"2025-11-02T23:01:35Z","month":"09","title":"Heat flow, log-concavity, and Lipschitz transport maps","PlanS_conform":"1","ddc":["500"],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"17353"}]},"article_number":"71","article_type":"original","doi":"10.1214/25-ECP717","year":"2025","author":[{"id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","full_name":"Brigati, Giovanni","last_name":"Brigati","first_name":"Giovanni"},{"last_name":"Pedrotti","first_name":"Francesco","full_name":"Pedrotti, Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"}],"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"scopus_import":"1","day":"25","DOAJ_listed":"1"},{"oa":1,"type":"journal_article","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"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s11118-025-10251-y"}],"date_created":"2025-12-14T23:02:03Z","arxiv":1,"quality_controlled":"1","status":"public","article_number":"6","article_type":"original","author":[{"full_name":"Keller, Matthias","last_name":"Keller","first_name":"Matthias"},{"first_name":"Daniel","last_name":"Lenz","full_name":"Lenz, Daniel"},{"full_name":"Schmidt, Marcel","last_name":"Schmidt","first_name":"Marcel"},{"last_name":"Schwarz","first_name":"Michael","full_name":"Schwarz, Michael"},{"last_name":"Wirth","first_name":"Melchior","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"},{"name":"Gradient flow techniques for quantum Markov semigroups","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N"}],"year":"2025","doi":"10.1007/s11118-025-10251-y","day":"03","scopus_import":"1","month":"12","title":"Boundary representations of intermediate forms between a regular Dirichlet form and its active main part","ddc":["510"],"PlanS_conform":"1","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).","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","intvolume":"        64","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"oa_version":"Published Version","date_published":"2025-12-03T00:00:00Z","volume":64,"publication_status":"epub_ahead","publisher":"Springer Nature","OA_type":"hybrid","OA_place":"publisher","language":[{"iso":"eng"}],"has_accepted_license":"1","external_id":{"arxiv":["2301.01035"]},"publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"citation":{"mla":"Keller, Matthias, et al. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>, vol. 64, 6, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s11118-025-10251-y\">10.1007/s11118-025-10251-y</a>.","ama":"Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. <i>Potential Analysis</i>. 2025;64. doi:<a href=\"https://doi.org/10.1007/s11118-025-10251-y\">10.1007/s11118-025-10251-y</a>","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).","apa":"Keller, M., Lenz, D., Schmidt, M., Schwarz, M., &#38; Wirth, M. (2025). Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-025-10251-y\">https://doi.org/10.1007/s11118-025-10251-y</a>","chicago":"Keller, Matthias, Daniel Lenz, Marcel Schmidt, Michael Schwarz, and Melchior Wirth. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s11118-025-10251-y\">https://doi.org/10.1007/s11118-025-10251-y</a>.","ieee":"M. Keller, D. Lenz, M. Schmidt, M. Schwarz, and M. Wirth, “Boundary representations of intermediate forms between a regular Dirichlet form and its active main part,” <i>Potential Analysis</i>, vol. 64. Springer Nature, 2025."},"department":[{"_id":"JaMa"}],"date_updated":"2025-12-15T13:11:24Z","article_processing_charge":"Yes (via OA deal)","_id":"20814"},{"department":[{"_id":"JaMa"}],"citation":{"ieee":"G. Auricchio, G. Brigati, P. Giudici, and G. Toscani, “Multivariate Gini-type discrepancies,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 35, no. 5. World Scientific Publishing, pp. 1267–1296, 2025.","chicago":"Auricchio, Gennaro, Giovanni Brigati, Paolo Giudici, and Giuseppe Toscani. “Multivariate Gini-Type Discrepancies.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2025. <a href=\"https://doi.org/10.1142/s0218202525500174\">https://doi.org/10.1142/s0218202525500174</a>.","ista":"Auricchio G, Brigati G, Giudici P, Toscani G. 2025. Multivariate Gini-type discrepancies. Mathematical Models and Methods in Applied Sciences. 35(5), 1267–1296.","short":"G. Auricchio, G. Brigati, P. Giudici, G. Toscani, Mathematical Models and Methods in Applied Sciences 35 (2025) 1267–1296.","mla":"Auricchio, Gennaro, et al. “Multivariate Gini-Type Discrepancies.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 35, no. 5, World Scientific Publishing, 2025, pp. 1267–96, doi:<a href=\"https://doi.org/10.1142/s0218202525500174\">10.1142/s0218202525500174</a>.","ama":"Auricchio G, Brigati G, Giudici P, Toscani G. Multivariate Gini-type discrepancies. <i>Mathematical Models and Methods in Applied Sciences</i>. 2025;35(5):1267-1296. doi:<a href=\"https://doi.org/10.1142/s0218202525500174\">10.1142/s0218202525500174</a>","apa":"Auricchio, G., Brigati, G., Giudici, P., &#38; Toscani, G. (2025). Multivariate Gini-type discrepancies. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0218202525500174\">https://doi.org/10.1142/s0218202525500174</a>"},"publication_identifier":{"eissn":["1793-6314"],"issn":["0218-2025"]},"external_id":{"arxiv":["2411.01052"],"isi":["001456337300001"]},"OA_type":"green","OA_place":"repository","language":[{"iso":"eng"}],"issue":"5","_id":"19565","article_processing_charge":"No","date_updated":"2025-09-30T11:36:56Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","intvolume":"        35","publication":"Mathematical Models and Methods in Applied Sciences","isi":1,"publisher":"World Scientific Publishing","publication_status":"published","volume":35,"date_published":"2025-05-01T00:00:00Z","oa_version":"Preprint","scopus_import":"1","page":"1267-1296","day":"01","year":"2025","doi":"10.1142/s0218202525500174","author":[{"full_name":"Auricchio, Gennaro","last_name":"Auricchio","first_name":"Gennaro"},{"last_name":"Brigati","first_name":"Giovanni","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","full_name":"Brigati, Giovanni"},{"full_name":"Giudici, Paolo","first_name":"Paolo","last_name":"Giudici"},{"full_name":"Toscani, Giuseppe","last_name":"Toscani","first_name":"Giuseppe"}],"article_type":"original","title":"Multivariate Gini-type discrepancies","month":"05","date_created":"2025-04-15T13:34:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2411.01052","open_access":"1"}],"abstract":[{"lang":"eng","text":"Measuring distances in a multidimensional setting is a challenging problem, which appears in many fields of science and engineering. In this paper, to measure the distance between two multivariate distributions, we introduce a new measure of discrepancy which is scale invariant and which, in the case of two independent copies of the same distribution, and after normalization, coincides with the scaling invariant multidimensional version of the Gini index recently proposed in [P. Giudici, E. Raffinetti and G. Toscani, Measuring multidimensional inequality: A new proposal based on the Fourier transform, preprint (2024), arXiv:2401.14012 ]. A byproduct of the analysis is an easy-to-handle discrepancy metric, obtained by application of the theory to a pair of Gaussian multidimensional densities. The obtained metric does improve the standard metrics, based on the mean squared error, as it is scale invariant. The importance of this theoretical finding is illustrated by means of a real problem that concerns measuring the importance of Environmental, Social and Governance factors for the growth of small and medium enterprises. "}],"type":"journal_article","oa":1,"status":"public","arxiv":1,"quality_controlled":"1"},{"quality_controlled":"1","arxiv":1,"status":"public","corr_author":"1","file":[{"relation":"main_file","creator":"dernst","access_level":"open_access","date_updated":"2025-05-05T09:20:54Z","checksum":"2948e8f567f20f5f837061d2c775534f","file_size":650764,"file_id":"19650","file_name":"2025_CommMathPhysics_Kumar.pdf","content_type":"application/pdf","date_created":"2025-05-05T09:20:54Z","success":1}],"oa":1,"type":"journal_article","abstract":[{"text":"We introduce operator-valued twisted Araki–Woods algebras. These are operator-valued versions of a class of second quantization algebras that includes q-Gaussian and q-Araki–Woods algebras and also generalize Shlyakhtenko’s von Neumann algebras generated by operator-valued semicircular variables. We develop a disintegration theory that reduces the isomorphism type of operator-valued twisted Araki–Woods algebras over type I factors to the scalar-valued case. Moreover, these algebras come with a natural weight, and we characterize its modular theory. We also give sufficient criteria that guarantee the factoriality of these algebras.","lang":"eng"}],"date_created":"2025-04-27T22:02:13Z","month":"05","title":"Operator-valued twisted Araki–Woods algebras","ddc":["510"],"article_number":"110","article_type":"original","doi":"10.1007/s00220-025-05285-7","year":"2025","project":[{"grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups"}],"author":[{"first_name":"R. Rahul","last_name":"Kumar","full_name":"Kumar, R. Rahul"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior","last_name":"Wirth","first_name":"Melchior","orcid":"0000-0002-0519-4241"}],"scopus_import":"1","day":"01","oa_version":"Published Version","date_published":"2025-05-01T00:00:00Z","volume":406,"publisher":"Springer Nature","publication_status":"published","isi":1,"acknowledgement":"The authors want to thank the organizers of YMC*A 2023 in Leuven, where this collaboration was conceived. They are grateful to Dan Voiculescu for a valuable historical remark and to Zhiyuan Yang for raising the question if operator-valued weights give rise to Tomita correspondences. R.K. was funded by IIT Kanpur through the Institute Postdoctoral Fellowship. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.\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"},"publication":"Communications in Mathematical Physics","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","intvolume":"       406","file_date_updated":"2025-05-05T09:20:54Z","article_processing_charge":"Yes (via OA deal)","date_updated":"2025-09-30T12:19:22Z","_id":"19625","issue":"5","has_accepted_license":"1","OA_type":"hybrid","language":[{"iso":"eng"}],"OA_place":"publisher","external_id":{"pmid":["40225194"],"arxiv":["2406.06179"],"isi":["001464170400003"]},"pmid":1,"department":[{"_id":"JaMa"}],"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"citation":{"apa":"Kumar, R. R., &#38; Wirth, M. (2025). Operator-valued twisted Araki–Woods algebras. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-025-05285-7\">https://doi.org/10.1007/s00220-025-05285-7</a>","ista":"Kumar RR, Wirth M. 2025. Operator-valued twisted Araki–Woods algebras. Communications in Mathematical Physics. 406(5), 110.","short":"R.R. Kumar, M. Wirth, Communications in Mathematical Physics 406 (2025).","mla":"Kumar, R. Rahul, and Melchior Wirth. “Operator-Valued Twisted Araki–Woods Algebras.” <i>Communications in Mathematical Physics</i>, vol. 406, no. 5, 110, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00220-025-05285-7\">10.1007/s00220-025-05285-7</a>.","ama":"Kumar RR, Wirth M. Operator-valued twisted Araki–Woods algebras. <i>Communications in Mathematical Physics</i>. 2025;406(5). doi:<a href=\"https://doi.org/10.1007/s00220-025-05285-7\">10.1007/s00220-025-05285-7</a>","ieee":"R. R. Kumar and M. Wirth, “Operator-valued twisted Araki–Woods algebras,” <i>Communications in Mathematical Physics</i>, vol. 406, no. 5. Springer Nature, 2025.","chicago":"Kumar, R. Rahul, and Melchior Wirth. “Operator-Valued Twisted Araki–Woods Algebras.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00220-025-05285-7\">https://doi.org/10.1007/s00220-025-05285-7</a>."}},{"month":"06","title":"Genetic load, eco-evolutionary feedback, and extinction in metapopulations","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"14732"}]},"article_type":"original","year":"2025","doi":"10.1086/735562","author":[{"full_name":"Olusanya, Oluwafunmilola O","id":"41AD96DC-F248-11E8-B48F-1D18A9856A87","first_name":"Oluwafunmilola O","last_name":"Olusanya","orcid":"0000-0003-1971-8314"},{"id":"4E6DC800-AE37-11E9-AC72-31CAE5697425","full_name":"Khudiakova, Kseniia","first_name":"Kseniia","last_name":"Khudiakova","orcid":"0000-0002-6246-1465"},{"last_name":"Sachdeva","first_name":"Himani","id":"42377A0A-F248-11E8-B48F-1D18A9856A87","full_name":"Sachdeva, Himani"}],"project":[{"name":"Causes and consequences of population fragmentation","_id":"c08d3278-5a5b-11eb-8a69-fdb09b55f4b8","grant_number":"P32896"},{"name":"Polygenic Adaptation in a Metapopulation","_id":"34c872fe-11ca-11ed-8bc3-8534b82131e6","grant_number":"26380"},{"_id":"34d33d68-11ca-11ed-8bc3-ec13763c0ca8","grant_number":"26293","name":"The impact of deleterious mutations on small populations"}],"page":"617-636","scopus_import":"1","day":"01","quality_controlled":"1","status":"public","corr_author":"1","oa":1,"type":"journal_article","main_file_link":[{"url":"https://doi.org/10.1101/2023.12.02.569702","open_access":"1"}],"abstract":[{"text":"Habitat fragmentation poses a significant risk to population survival, causing both demographic stochasticity and genetic drift within local populations to increase, thereby increasing genetic load. Higher load causes population numbers to decline, which reduces the efficiency of selection and further increases load, resulting in a positive feedback that may drive entire populations to extinction. Here, we investigate this eco-evolutionary feedback in a metapopulation consisting of local demes connected via migration, with individuals subject to deleterious mutation at a large number of loci. We first analyze the determinants of load under soft selection, where population sizes are fixed, and then build on this to understand hard selection, where population sizes and load coevolve. We show that under soft selection, very little gene flow (less than one migrant per generation) is enough to prevent fixation of deleterious alleles. By contrast, much higher levels of migration are required to mitigate load and prevent extinction when selection is hard, with critical migration thresholds for metapopulation persistence increasing sharply as the genome-wide deleterious mutation rate becomes comparable to the baseline population growth rate. Moreover, critical migration thresholds are highest if deleterious mutations have intermediate selection coefficients but lower if alleles are predominantly recessive rather than additive (due to more efficient purging of recessive load within local populations). Our analysis is based on a combination of analytical approximations and simulations, allowing for a more comprehensive understanding of the factors influencing load and extinction in fragmented populations.","lang":"eng"}],"date_created":"2026-02-18T10:47:18Z","article_processing_charge":"No","date_updated":"2026-04-07T08:45:14Z","_id":"21322","issue":"6","OA_type":"green","OA_place":"repository","language":[{"iso":"eng"}],"external_id":{"pmid":["40446297 "]},"pmid":1,"department":[{"_id":"JaMa"},{"_id":"NiBa"}],"citation":{"chicago":"Olusanya, Oluwafunmilola O, Kseniia Khudiakova, and Himani Sachdeva. “Genetic Load, Eco-Evolutionary Feedback, and Extinction in Metapopulations.” <i>The American Naturalist</i>. University of Chicago Press, 2025. <a href=\"https://doi.org/10.1086/735562\">https://doi.org/10.1086/735562</a>.","ieee":"O. O. Olusanya, K. Khudiakova, and H. Sachdeva, “Genetic load, eco-evolutionary feedback, and extinction in metapopulations,” <i>The American Naturalist</i>, vol. 205, no. 6. University of Chicago Press, pp. 617–636, 2025.","apa":"Olusanya, O. O., Khudiakova, K., &#38; Sachdeva, H. (2025). Genetic load, eco-evolutionary feedback, and extinction in metapopulations. <i>The American Naturalist</i>. University of Chicago Press. <a href=\"https://doi.org/10.1086/735562\">https://doi.org/10.1086/735562</a>","mla":"Olusanya, Oluwafunmilola O., et al. “Genetic Load, Eco-Evolutionary Feedback, and Extinction in Metapopulations.” <i>The American Naturalist</i>, vol. 205, no. 6, University of Chicago Press, 2025, pp. 617–36, doi:<a href=\"https://doi.org/10.1086/735562\">10.1086/735562</a>.","ama":"Olusanya OO, Khudiakova K, Sachdeva H. Genetic load, eco-evolutionary feedback, and extinction in metapopulations. <i>The American Naturalist</i>. 2025;205(6):617-636. doi:<a href=\"https://doi.org/10.1086/735562\">10.1086/735562</a>","ista":"Olusanya OO, Khudiakova K, Sachdeva H. 2025. Genetic load, eco-evolutionary feedback, and extinction in metapopulations. The American Naturalist. 205(6), 617–636.","short":"O.O. Olusanya, K. Khudiakova, H. Sachdeva, The American Naturalist 205 (2025) 617–636."},"publication_identifier":{"eissn":["1537-5323"],"issn":["0003-0147"]},"oa_version":"Preprint","date_published":"2025-06-01T00:00:00Z","volume":205,"publisher":"University of Chicago Press","publication_status":"published","acknowledgement":"This research was partially funded by the Austrian Science Fund (FWF P-32896B) and DOC Fellowships of the Austrian Academy of Sciences: grants 26380 (O.O.) and 26293 (K.K.). We thank Nick Barton for useful comments on the chapter in O.O.’s thesis that led to this article.","publication":"The American Naturalist","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","intvolume":"       205"},{"_id":"20563","date_updated":"2026-04-07T12:39:35Z","article_processing_charge":"No","citation":{"apa":"Quattrocchi, F. (2025). <i>Optimal transport methods for kinetic equations, boundary value problems, and discretization of measures</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-20563\">https://doi.org/10.15479/AT-ISTA-20563</a>","ista":"Quattrocchi F. 2025. Optimal transport methods for kinetic equations, boundary value problems, and discretization of measures. Institute of Science and Technology Austria.","short":"F. Quattrocchi, Optimal Transport Methods for Kinetic Equations, Boundary Value Problems, and Discretization of Measures, Institute of Science and Technology Austria, 2025.","ama":"Quattrocchi F. Optimal transport methods for kinetic equations, boundary value problems, and discretization of measures. 2025. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-20563\">10.15479/AT-ISTA-20563</a>","mla":"Quattrocchi, Filippo. <i>Optimal Transport Methods for Kinetic Equations, Boundary Value Problems, and Discretization of Measures</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-20563\">10.15479/AT-ISTA-20563</a>.","ieee":"F. Quattrocchi, “Optimal transport methods for kinetic equations, boundary value problems, and discretization of measures,” Institute of Science and Technology Austria, 2025.","chicago":"Quattrocchi, Filippo. “Optimal Transport Methods for Kinetic Equations, Boundary Value Problems, and Discretization of Measures.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/AT-ISTA-20563\">https://doi.org/10.15479/AT-ISTA-20563</a>."},"publication_identifier":{"issn":["2663-337X"]},"department":[{"_id":"GradSch"},{"_id":"JaMa"}],"language":[{"iso":"eng"}],"OA_place":"publisher","has_accepted_license":"1","publication_status":"published","publisher":"Institute of Science and Technology Austria","date_published":"2025-11-03T00:00:00Z","oa_version":"Published Version","file_date_updated":"2026-01-01T23:30:03Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","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"},"alternative_title":["ISTA Thesis"],"acknowledgement":"The research contained in this thesis has received funding from the Austrian Science\r\nFund (FWF) project 10.55776/F65.","supervisor":[{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338"}],"related_material":{"record":[{"id":"18706","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"20569"},{"id":"20571","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"20570"}]},"degree_awarded":"PhD","ddc":["515","519"],"title":"Optimal transport methods for kinetic equations, boundary value problems, and discretization of measures","month":"11","day":"03","page":"240","author":[{"orcid":"0009-0000-9773-1931","last_name":"Quattrocchi","first_name":"Filippo","id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308","full_name":"Quattrocchi, Filippo"}],"project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F06504","call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425"}],"year":"2025","doi":"10.15479/AT-ISTA-20563","corr_author":"1","status":"public","date_created":"2025-10-28T13:10:49Z","abstract":[{"lang":"eng","text":"The theory of optimal transport provides an elegant and powerful description of many evolution\r\nequations as gradient flows. The primary objective of this thesis is to adapt and extend the\r\ntheory to deal with important equations that are not covered by the classical framework,\r\nspecifically boundary value problems and kinetic equations. Additionally, we establish new\r\nresults in periodic homogenization for discrete dynamical optimal transport and in quantization\r\nof measures.\r\nSection 1.1 serves as an invitation to the classical theory of optimal transport, including the\r\nmain definitions and a selection of well-established theorems. Sections 1.2-1.5 introduce the\r\nmain results of this thesis, outline the motivations, and review the current state of the art.\r\nIn Chapter 2, we consider the Fokker–Planck equation on a bounded set with positive Dirichlet\r\nboundary conditions. We construct a time-discrete scheme involving a modification of the\r\nWasserstein distance and, under weak assumptions, prove its convergence to a solution of this\r\nboundary value problem. In dimension 1, we show that this solution is a gradient flow in a\r\nsuitable space of measures.\r\nChapter 3 presents joint work with Giovanni Brigati and Jan Maas. We introduce a new theory\r\nof optimal transport to describe and study particle systems at the mesoscopic scale. We prove\r\nadapted versions of some fundamental theorems, including the Benamou–Brenier formula and\r\nthe identification of absolutely continuous curves of measures.\r\nChapter 4 presents joint work with Lorenzo Portinale. We prove convergence of dynamical\r\ntransportation functionals on periodic graphs in the large-scale limit when the cost functional\r\nis asymptotically linear. Additionally, we show that discrete 1-Wasserstein distances converge\r\nto 1-Wasserstein distances constructed from crystalline norms on R\r\nd\r\n.\r\nChapter 5 concerns optimal empirical quantization: the problem of approximating a measure\r\nby the sum of n equally weighted Dirac deltas, so as to minimize the error in the p-Wasserstein\r\ndistance. Our main result is an analog of Zador’s theorem, providing asymptotic bounds for\r\nthe minimal error as n tends to infinity.\r\n"}],"type":"dissertation","keyword":["optimal transport","kinetic equations","boundary value problems","quantization","gradient flows","homogenization"],"file":[{"creator":"fquattro","access_level":"open_access","date_updated":"2026-01-01T23:30:03Z","relation":"main_file","file_id":"20653","checksum":"6f55275bdf99992be3a6457d949dd664","file_size":4326411,"embargo":"2026-01-01","file_name":"2025_quattrocchi_filippo_thesis.pdf","date_created":"2025-11-17T21:04:15Z","content_type":"application/pdf"},{"date_created":"2025-11-17T21:05:43Z","content_type":"application/zip","embargo_to":"open_access","file_name":"2025_quattrocchi_thesis.zip","relation":"source_file","date_updated":"2026-01-01T23:30:03Z","creator":"fquattro","access_level":"closed","file_size":11726509,"checksum":"707e580f5d993a214c0dba456b75837b","file_id":"20654"}],"oa":1},{"acknowledgement":"This work was partially inspired by an unpublished note from 2014 by Guillaume Carlier,\r\nJean Dolbeault, and Bruno Nazaret. GB deeply thanks Jean Dolbeault for proposing\r\nthis problem to him, guiding him into the subject, and sharing the aforementioned note.\r\nWe are grateful to Karthik Elamvazhuthi for making us aware of the work [20].\r\nThe work of GB has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement\r\nNo 101034413.\r\nJM and FQ gratefully acknowledge support from the Austrian Science Fund (FWF)\r\nproject 10.55776/F65.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"arXiv","date_published":"2025-08-10T00:00:00Z","oa_version":"Preprint","ec_funded":1,"publication_status":"draft","OA_place":"repository","language":[{"iso":"eng"}],"OA_type":"green","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"citation":{"mla":"Brigati, Giovanni, et al. “Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-Order Discrepancies between Probability Measures.” <i>ArXiv</i>, 2502.15665, doi:<a href=\"https://doi.org/10.48550/arXiv.2502.15665\">10.48550/arXiv.2502.15665</a>.","ama":"Brigati G, Maas J, Quattrocchi F. Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between probability measures. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2502.15665\">10.48550/arXiv.2502.15665</a>","ista":"Brigati G, Maas J, Quattrocchi F. Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between probability measures. arXiv, 2502.15665.","short":"G. Brigati, J. Maas, F. Quattrocchi, ArXiv (n.d.).","apa":"Brigati, G., Maas, J., &#38; Quattrocchi, F. (n.d.). Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between probability measures. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2502.15665\">https://doi.org/10.48550/arXiv.2502.15665</a>","chicago":"Brigati, Giovanni, Jan Maas, and Filippo Quattrocchi. “Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-Order Discrepancies between Probability Measures.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2502.15665\">https://doi.org/10.48550/arXiv.2502.15665</a>.","ieee":"G. Brigati, J. Maas, and F. Quattrocchi, “Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between probability measures,” <i>arXiv</i>. ."},"external_id":{"arxiv":["2502.15665"]},"_id":"20569","article_processing_charge":"No","date_updated":"2026-04-29T22:30:16Z","type":"preprint","oa":1,"keyword":["optimal transport","kinetic theory","second-order discrepancy","Vlasov equation","Wasserstein splines."],"date_created":"2025-10-28T13:12:08Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2502.15665"}],"abstract":[{"lang":"eng","text":"This is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framework naturally applies in biology, computer vision, and engineering. The central object of our study is a new discrepancy d between two probability distributions in position and velocity states, which is reminiscent of the 2-Wasserstein distance, but of second-order nature. We construct d in two steps. First, we optimise over transport plans. The cost function is given by the minimal acceleration between two coupled states on a fixed time horizon T. Second, we further optimise over the time horizon T > 0. We prove the existence of optimal transport plans and maps, and study two time-continuous characterisations of d. One is given in terms of dynamical transport plans. The other one -- in the spirit of the Benamou--Brenier formula -- is formulated as the minimisation of an action of the acceleration field, constrained by Vlasov's equations. Equivalence of static and dynamical formulations of d holds true. While part of this result can be derived from recent, parallel developments in optimal control between measures, we give an original proof relying on two new ingredients: Galilean regularisation of Vlasov's equations and a kinetic Monge--Mather shortening principle. Finally, we establish a first-order differential calculus in the geometry induced by d, and identify solutions to Vlasov's equations with curves of measures satisfying a certain d-absolute continuity condition. One consequence is an explicit formula for the d-derivative of such curves."}],"status":"public","arxiv":1,"corr_author":"1","article_number":"2502.15665","day":"10","year":"2025","doi":"10.48550/arXiv.2502.15665","author":[{"full_name":"Brigati, Giovanni","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","first_name":"Giovanni","last_name":"Brigati"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan"},{"last_name":"Quattrocchi","first_name":"Filippo","orcid":"0009-0000-9773-1931","id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308","full_name":"Quattrocchi, Filippo"}],"project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"title":"Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between probability measures","month":"08","related_material":{"record":[{"id":"20563","relation":"dissertation_contains","status":"public"}]}},{"corr_author":"1","quality_controlled":"1","arxiv":1,"status":"public","abstract":[{"lang":"eng","text":"We study the geometry of Poisson point processes from the point of view of optimal transport and Ricci lower bounds. We construct a Riemannian structure on the space of point processes and the associated distance W that corresponds to the Benamou–Brenier variational formula. Our main tool is a non-local continuity equation formulated with the difference operator. The closure of the domain of the relative entropy is a complete geodesic space, when endowed with \r\nW. The geometry of this non-local infinite-dimensional space is analogous to that of spaces with positive Ricci curvature. Among others: (a) the Ornstein–Uhlenbeck semi-group is the gradient flow of the relative entropy; (b) the Poisson space has an entropic Ricci curvature bounded from below by 1; (c) W satisfies an HWI inequality."},{"lang":"fre","text":"Nous étudions la géométrie des processus ponctuels de Poisson à travers le prisme du transport optimal et de la minoration de la courbure de Ricci. Nous construisons une structure\r\nriemannienne sur l’espace des processus ponctuels et la distance associée W qui concorde avec la formulation variationnelle de Benamou–Brenier. Notre analyse repose sur une équation de continuité non locale définie à l’aide de l’opérateur de différence. La fermeture du domaine de l’entropie relative, équipé de W, est un espace géodésique complet. La géométrie de cet espace non local et de dimension infinie est analogue à celle des espaces à courbure de Ricci strictement positive. Entre autres : (a) le semi-groupe d’Ornstein–Uhlenbeck est le flot du gradient de l’entropie relative ; (b) l’espace de Poisson a une courbure de Ricci entropique minorée par 1 ; (c) W satisfait une inégalité HWI."}],"date_created":"2024-09-29T22:01:38Z","oa":1,"file":[{"success":1,"file_name":"2024_JourEcolePolytechniqueMath_DelloSchiavo.pdf","date_created":"2024-10-01T07:31:56Z","content_type":"application/pdf","creator":"dernst","access_level":"open_access","date_updated":"2024-10-01T07:31:56Z","relation":"main_file","file_id":"18164","checksum":"5a51da5fb5f7fcaada378d43444cced8","file_size":1250553}],"type":"journal_article","ddc":["510"],"month":"01","title":"Wasserstein geometry and Ricci curvature bounds for Poisson spaces","author":[{"first_name":"Lorenzo","last_name":"Dello Schiavo","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":"Suzuki","first_name":"Kohei","full_name":"Suzuki, Kohei"}],"doi":"10.5802/jep.270","year":"2024","day":"01","page":"957-1010","scopus_import":"1","article_type":"original","publication_status":"published","publisher":"Ecole Polytechnique","oa_version":"Published Version","volume":11,"date_published":"2024-01-01T00:00:00Z","publication":"Journal de l'Ecole Polytechnique - Mathematiques","file_date_updated":"2024-10-01T07:31:56Z","intvolume":"        11","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","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":"2025-09-08T09:50:50Z","article_processing_charge":"Yes","_id":"18158","external_id":{"isi":["001367254000003"],"arxiv":["2303.00398"]},"publication_identifier":{"eissn":["2270-518X"],"issn":["2429-7100"]},"citation":{"ama":"Dello Schiavo L, Herry R, Suzuki K. Wasserstein geometry and Ricci curvature bounds for Poisson spaces. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. 2024;11:957-1010. doi:<a href=\"https://doi.org/10.5802/jep.270\">10.5802/jep.270</a>","mla":"Dello Schiavo, Lorenzo, et al. “Wasserstein Geometry and Ricci Curvature Bounds for Poisson Spaces.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 11, Ecole Polytechnique, 2024, pp. 957–1010, doi:<a href=\"https://doi.org/10.5802/jep.270\">10.5802/jep.270</a>.","ista":"Dello Schiavo L, Herry R, Suzuki K. 2024. Wasserstein geometry and Ricci curvature bounds for Poisson spaces. Journal de l’Ecole Polytechnique - Mathematiques. 11, 957–1010.","short":"L. Dello Schiavo, R. Herry, K. Suzuki, Journal de l’Ecole Polytechnique - Mathematiques 11 (2024) 957–1010.","apa":"Dello Schiavo, L., Herry, R., &#38; Suzuki, K. (2024). Wasserstein geometry and Ricci curvature bounds for Poisson spaces. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. Ecole Polytechnique. <a href=\"https://doi.org/10.5802/jep.270\">https://doi.org/10.5802/jep.270</a>","chicago":"Dello Schiavo, Lorenzo, Ronan Herry, and Kohei Suzuki. “Wasserstein Geometry and Ricci Curvature Bounds for Poisson Spaces.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. Ecole Polytechnique, 2024. <a href=\"https://doi.org/10.5802/jep.270\">https://doi.org/10.5802/jep.270</a>.","ieee":"L. Dello Schiavo, R. Herry, and K. Suzuki, “Wasserstein geometry and Ricci curvature bounds for Poisson spaces,” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 11. Ecole Polytechnique, pp. 957–1010, 2024."},"department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"has_accepted_license":"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"}],"type":"journal_article","oa":1,"file":[{"checksum":"143816823b5f43bd3748da8e3e91cef5","file_size":911476,"file_id":"18497","relation":"main_file","access_level":"open_access","creator":"dernst","date_updated":"2024-11-04T08:54:26Z","file_name":"2024_JourLondonMathSoc_Schiavo.pdf","content_type":"application/pdf","date_created":"2024-11-04T08:54:26Z","success":1}],"status":"public","quality_controlled":"1","day":"01","scopus_import":"1","author":[{"orcid":"0000-0002-9881-6870","first_name":"Lorenzo","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"first_name":"Ronan","last_name":"Herry","full_name":"Herry, Ronan"},{"first_name":"Eva","last_name":"Kopfer","full_name":"Kopfer, Eva"},{"last_name":"Sturm","first_name":"Karl Theodor","full_name":"Sturm, Karl Theodor"}],"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"doi":"10.1112/jlms.70003","year":"2024","article_type":"original","article_number":"e70003","ddc":["510"],"title":"Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension","month":"11","file_date_updated":"2024-11-04T08:54:26Z","intvolume":"       110","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication":"Journal of the London Mathematical Society","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":"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.","isi":1,"publication_status":"published","publisher":"London Mathematical Society","volume":110,"date_published":"2024-11-01T00:00:00Z","ec_funded":1,"oa_version":"Published Version","publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"citation":{"chicago":"Dello Schiavo, Lorenzo, Ronan Herry, Eva Kopfer, and Karl Theodor Sturm. “Conformally Invariant Random Fields, Liouville Quantum Gravity Measures, and Random Paneitz Operators on Riemannian Manifolds of Even Dimension.” <i>Journal of the London Mathematical Society</i>. London Mathematical Society, 2024. <a href=\"https://doi.org/10.1112/jlms.70003\">https://doi.org/10.1112/jlms.70003</a>.","ieee":"L. Dello Schiavo, R. Herry, E. Kopfer, and K. T. Sturm, “Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension,” <i>Journal of the London Mathematical Society</i>, vol. 110, no. 5. London Mathematical Society, 2024.","apa":"Dello Schiavo, L., Herry, R., Kopfer, E., &#38; Sturm, K. T. (2024). Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension. <i>Journal of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/jlms.70003\">https://doi.org/10.1112/jlms.70003</a>","mla":"Dello Schiavo, Lorenzo, et al. “Conformally Invariant Random Fields, Liouville Quantum Gravity Measures, and Random Paneitz Operators on Riemannian Manifolds of Even Dimension.” <i>Journal of the London Mathematical Society</i>, vol. 110, no. 5, e70003, London Mathematical Society, 2024, doi:<a href=\"https://doi.org/10.1112/jlms.70003\">10.1112/jlms.70003</a>.","ama":"Dello Schiavo L, Herry R, Kopfer E, Sturm KT. Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension. <i>Journal of the London Mathematical Society</i>. 2024;110(5). doi:<a href=\"https://doi.org/10.1112/jlms.70003\">10.1112/jlms.70003</a>","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)."},"department":[{"_id":"JaMa"}],"external_id":{"isi":["001351918100029"]},"OA_type":"hybrid","language":[{"iso":"eng"}],"OA_place":"publisher","has_accepted_license":"1","issue":"5","_id":"18490","date_updated":"2025-09-08T14:29:45Z","article_processing_charge":"Yes (via OA deal)"},{"status":"public","quality_controlled":"1","arxiv":1,"corr_author":"1","type":"journal_article","oa":1,"date_created":"2023-07-23T22:01:15Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2108.05785","open_access":"1"}],"abstract":[{"lang":"eng","text":"In this paper, we prove the convexity of trace functionals (A,B,C)↦Tr|BpACq|s,\r\nfor parameters (p, q, s) that are best possible, where B and C are any n-by-n positive-definite matrices, and A is any n-by-n matrix. We also obtain the monotonicity versions of trace functionals of this type. As applications, we extend some results in Carlen et al. (Linear Algebra Appl 490:174–185, 2016), Hiai and Petz (Publ Res Inst Math Sci 48(3):525-542, 2012) and resolve a conjecture in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) in the matrix setting. Other conjectures in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) will also be discussed. We also show that some related trace functionals are not concave in general. Such concavity results were expected to hold in different problems."}],"title":"Some convexity and monotonicity results of trace functionals","month":"04","article_type":"original","scopus_import":"1","page":"2087-2106","day":"01","doi":"10.1007/s00023-023-01345-7","year":"2024","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis"}],"author":[{"last_name":"Zhang","first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan"}],"date_published":"2024-04-01T00:00:00Z","volume":25,"oa_version":"Preprint","ec_funded":1,"publisher":"Springer Nature","publication_status":"published","isi":1,"acknowledgement":"I am grateful to Boguslaw Zegarliński for asking me the questions in [3] and for helpful communication. I also want to thank Paata Ivanisvili for drawing [25] to my attention and for useful correspondence. Many thanks to the anonymous referee for the valuable comments and for pointing out some errors in an earlier version of the paper. This work is partially 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.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        25","publication":"Annales Henri Poincare","_id":"13271","article_processing_charge":"No","date_updated":"2025-04-14T07:43:55Z","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"publication_identifier":{"issn":["1424-0637"]},"citation":{"chicago":"Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.” <i>Annales Henri Poincare</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00023-023-01345-7\">https://doi.org/10.1007/s00023-023-01345-7</a>.","ieee":"H. Zhang, “Some convexity and monotonicity results of trace functionals,” <i>Annales Henri Poincare</i>, vol. 25. Springer Nature, pp. 2087–2106, 2024.","apa":"Zhang, H. (2024). Some convexity and monotonicity results of trace functionals. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-023-01345-7\">https://doi.org/10.1007/s00023-023-01345-7</a>","ama":"Zhang H. Some convexity and monotonicity results of trace functionals. <i>Annales Henri Poincare</i>. 2024;25:2087-2106. doi:<a href=\"https://doi.org/10.1007/s00023-023-01345-7\">10.1007/s00023-023-01345-7</a>","mla":"Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.” <i>Annales Henri Poincare</i>, vol. 25, Springer Nature, 2024, pp. 2087–106, doi:<a href=\"https://doi.org/10.1007/s00023-023-01345-7\">10.1007/s00023-023-01345-7</a>.","short":"H. Zhang, Annales Henri Poincare 25 (2024) 2087–2106.","ista":"Zhang H. 2024. Some convexity and monotonicity results of trace functionals. Annales Henri Poincare. 25, 2087–2106."},"external_id":{"arxiv":["2108.05785"],"isi":["001025709100001"]}},{"publisher":"Springer Nature","publication_status":"published","volume":389,"date_published":"2024-06-01T00:00:00Z","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       389","file_date_updated":"2024-07-22T09:38:15Z","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 research of A.V. is supported by NSF DMS-1900286, DMS-2154402 and by Hausdorff Center for Mathematics. H.Z. is supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. This work is partially supported by NSF DMS-1929284 while both authors were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Harmonic Analysis and Convexity program.","_id":"13318","article_processing_charge":"Yes (in subscription journal)","date_updated":"2025-04-23T07:50:55Z","pmid":1,"department":[{"_id":"JaMa"}],"publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"citation":{"ieee":"A. Volberg and H. Zhang, “Noncommutative Bohnenblust–Hille inequalities,” <i>Mathematische Annalen</i>, vol. 389. Springer Nature, pp. 1657–1676, 2024.","chicago":"Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” <i>Mathematische Annalen</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00208-023-02680-0\">https://doi.org/10.1007/s00208-023-02680-0</a>.","short":"A. Volberg, H. Zhang, Mathematische Annalen 389 (2024) 1657–1676.","ista":"Volberg A, Zhang H. 2024. Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen. 389, 1657–1676.","ama":"Volberg A, Zhang H. Noncommutative Bohnenblust–Hille inequalities. <i>Mathematische Annalen</i>. 2024;389:1657-1676. doi:<a href=\"https://doi.org/10.1007/s00208-023-02680-0\">10.1007/s00208-023-02680-0</a>","mla":"Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” <i>Mathematische Annalen</i>, vol. 389, Springer Nature, 2024, pp. 1657–76, doi:<a href=\"https://doi.org/10.1007/s00208-023-02680-0\">10.1007/s00208-023-02680-0</a>.","apa":"Volberg, A., &#38; Zhang, H. (2024). Noncommutative Bohnenblust–Hille inequalities. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-023-02680-0\">https://doi.org/10.1007/s00208-023-02680-0</a>"},"external_id":{"isi":["001035665500001"],"arxiv":["2210.14468"],"pmid":["38751410"]},"has_accepted_license":"1","language":[{"iso":"eng"}],"corr_author":"1","status":"public","quality_controlled":"1","arxiv":1,"date_created":"2023-07-30T22:01:03Z","abstract":[{"lang":"eng","text":"Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow subexponentially in the degree (Defant et al. in Math Ann 374(1):653–680, 2019). Such inequalities have found great applications in learning low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions, 2022. arXiv preprint arXiv:2209.07279). The conjecture was resolved in Huang et al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894). In this paper, we give a new proof of these Bohnenblust–Hille inequalities for qubit system with constants that are dimension-free and of exponential growth in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials. Using similar ideas, we also study learning problems of low degree quantum observables and Bohr’s radius phenomenon on quantum Boolean cubes."}],"type":"journal_article","file":[{"success":1,"file_name":"2024_MathAnnalen_Volberg.pdf","date_created":"2024-07-22T09:38:15Z","content_type":"application/pdf","creator":"dernst","access_level":"open_access","date_updated":"2024-07-22T09:38:15Z","relation":"main_file","file_id":"17299","checksum":"56e67756e4c6c97589a8385e15ea2d2a","file_size":351796}],"oa":1,"ddc":["510"],"title":"Noncommutative Bohnenblust–Hille inequalities","month":"06","scopus_import":"1","page":"1657-1676","day":"01","doi":"10.1007/s00208-023-02680-0","year":"2024","author":[{"first_name":"Alexander","last_name":"Volberg","full_name":"Volberg, Alexander"},{"last_name":"Zhang","first_name":"Haonan","full_name":"Zhang, Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"project":[{"name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"}],"article_type":"original"},{"publication_status":"published","date_published":"2024-06-01T00:00:00Z","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2025-01-27T12:19:44Z","publication":"Transactions on Machine Learning Research","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"},"alternative_title":["TMLR"],"acknowledgement":"Francesco Pedrotti and Jan Maas acknowledge support by the Austrian Science Fund (FWF) project 10.55776/F65. Marco Mondelli acknowledges support by the 2019 Lopez-Loreta prize.\r\n","_id":"18897","article_processing_charge":"No","date_updated":"2025-04-15T08:31:35Z","department":[{"_id":"JaMa"},{"_id":"MaMo"}],"citation":{"apa":"Pedrotti, F., Maas, J., &#38; Mondelli, M. (2024). Improved convergence of score-based diffusion models via prediction-correction. In <i>Transactions on Machine Learning Research</i>.","ista":"Pedrotti F, Maas J, Mondelli M. 2024. Improved convergence of score-based diffusion models via prediction-correction. Transactions on Machine Learning Research. , TMLR, .","short":"F. Pedrotti, J. Maas, M. Mondelli, in:, Transactions on Machine Learning Research, 2024.","mla":"Pedrotti, Francesco, et al. “Improved Convergence of Score-Based Diffusion Models via Prediction-Correction.” <i>Transactions on Machine Learning Research</i>, 2024.","ama":"Pedrotti F, Maas J, Mondelli M. Improved convergence of score-based diffusion models via prediction-correction. In: <i>Transactions on Machine Learning Research</i>. ; 2024.","ieee":"F. Pedrotti, J. Maas, and M. Mondelli, “Improved convergence of score-based diffusion models via prediction-correction,” in <i>Transactions on Machine Learning Research</i>, 2024.","chicago":"Pedrotti, Francesco, Jan Maas, and Marco Mondelli. “Improved Convergence of Score-Based Diffusion Models via Prediction-Correction.” In <i>Transactions on Machine Learning Research</i>, 2024."},"publication_identifier":{"issn":["2835-8856"]},"external_id":{"arxiv":["2305.14164"]},"has_accepted_license":"1","OA_type":"gold","language":[{"iso":"eng"}],"OA_place":"publisher","corr_author":"1","status":"public","arxiv":1,"quality_controlled":"1","date_created":"2025-01-27T12:18:05Z","abstract":[{"lang":"eng","text":"Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time T1 by adding noise to the data, (ii) estimate its score function, and (iii) use such estimate to run a reverse process. As the reverse process is initialized with the stationary distribution of the forward one, the existing analysis paradigm requires T1→∞. This is however problematic: from a theoretical viewpoint, for a given precision of the score approximation, the convergence guarantee fails as T1 diverges; from a practical viewpoint, a large T1 increases computational costs and leads to error propagation. This paper addresses the issue by considering a version of the popular predictor-corrector scheme: after running the forward process, we first estimate the final distribution via an inexact Langevin dynamics and then revert the process. Our key technical contribution is to provide convergence guarantees which require to run the forward process only for a fixed finite time T1. Our bounds exhibit a mild logarithmic dependence on the input dimension and the subgaussian norm of the target distribution, have minimal assumptions on the data, and require only to control the L2 loss on the score approximation, which is the quantity minimized in practice."}],"type":"conference","file":[{"file_id":"18898","checksum":"76a1fd5afd8ee6f7ae0e5912d7dbf6b4","file_size":780315,"creator":"dernst","access_level":"open_access","date_updated":"2025-01-27T12:19:44Z","relation":"main_file","success":1,"file_name":"2024_TMLR_Pedrotti.pdf","date_created":"2025-01-27T12:19:44Z","content_type":"application/pdf"}],"oa":1,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"17350"}]},"ddc":["000"],"title":"Improved convergence of score-based diffusion models via prediction-correction","month":"06","scopus_import":"1","day":"01","year":"2024","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"_id":"059876FA-7A3F-11EA-A408-12923DDC885E","name":"Prix Lopez-Loretta 2019 - Marco Mondelli"}],"author":[{"last_name":"Pedrotti","first_name":"Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","full_name":"Pedrotti, Francesco"},{"orcid":"0000-0002-0845-1338","first_name":"Jan","last_name":"Maas","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mondelli, Marco","id":"27EB676C-8706-11E9-9510-7717E6697425","orcid":"0000-0002-3242-7020","last_name":"Mondelli","first_name":"Marco"}]}]