[{"external_id":{"isi":["000704213400001"],"arxiv":["2003.01366"]},"file":[{"creator":"dernst","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_name":"2023_PotentialAnalysis_DelloSchiavo.pdf","file_size":806391,"date_created":"2023-10-04T09:18:59Z","checksum":"625526482be300ca7281c91c30d41725","file_id":"14387","success":1,"date_updated":"2023-10-04T09:18:59Z"}],"title":"Ergodic decomposition of Dirichlet forms via direct integrals and applications","publication":"Potential Analysis","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"arxiv":1,"citation":{"ista":"Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 58, 573–615.","apa":"Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct integrals and applications. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-021-09951-y\">https://doi.org/10.1007/s11118-021-09951-y</a>","short":"L. Dello Schiavo, Potential Analysis 58 (2023) 573–615.","mla":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” <i>Potential Analysis</i>, vol. 58, Springer Nature, 2023, pp. 573–615, doi:<a href=\"https://doi.org/10.1007/s11118-021-09951-y\">10.1007/s11118-021-09951-y</a>.","ama":"Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals and applications. <i>Potential Analysis</i>. 2023;58:573-615. doi:<a href=\"https://doi.org/10.1007/s11118-021-09951-y\">10.1007/s11118-021-09951-y</a>","chicago":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” <i>Potential Analysis</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s11118-021-09951-y\">https://doi.org/10.1007/s11118-021-09951-y</a>.","ieee":"L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals and applications,” <i>Potential Analysis</i>, vol. 58. Springer Nature, pp. 573–615, 2023."},"has_accepted_license":"1","scopus_import":"1","ec_funded":1,"abstract":[{"lang":"eng","text":"We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique."}],"page":"573-615","publication_status":"published","oa_version":"Published Version","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"date_updated":"2023-10-04T09:19:12Z","status":"public","quality_controlled":"1","publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"month":"03","article_type":"original","volume":58,"isi":1,"department":[{"_id":"JaMa"}],"acknowledgement":"The author is grateful to Professors Sergio Albeverio and Andreas Eberle, and to Dr. Kohei Suzuki, for fruitful conversations on the subject of the present work, and for respectively pointing out the references [1, 13], and [3, 20]. Finally, he is especially grateful to an anonymous Reviewer for their very careful reading and their suggestions which improved the readability of the paper.","date_created":"2021-10-17T22:01:17Z","intvolume":"        58","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2023-10-04T09:18:59Z","oa":1,"_id":"10145","author":[{"orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","last_name":"Dello Schiavo","first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo"}],"date_published":"2023-03-01T00:00:00Z","publisher":"Springer Nature","year":"2023","language":[{"iso":"eng"}],"doi":"10.1007/s11118-021-09951-y","type":"journal_article"},{"ddc":["510"],"article_processing_charge":"Yes (via OA deal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2023-08-14T11:38:28Z","intvolume":"        24","date_created":"2022-09-11T22:01:57Z","department":[{"_id":"JaMa"}],"acknowledgement":"H.Z. is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. M.W. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117) and from the Austrian Science Fund (FWF) through grant number F65. Both authors would like to thank Jan Maas for fruitful discussions and helpful comments. Open access funding provided by Austrian Science Fund (FWF).","isi":1,"article_type":"original","volume":24,"month":"03","quality_controlled":"1","publication_identifier":{"issn":["1424-0637"]},"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s00023-022-01220-x","publisher":"Springer Nature","year":"2023","date_published":"2023-03-01T00:00:00Z","author":[{"full_name":"Wirth, Melchior","first_name":"Melchior","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241"},{"last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan","first_name":"Haonan"}],"oa":1,"_id":"12087","scopus_import":"1","has_accepted_license":"1","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"},{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337"},{"call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"arxiv":1,"citation":{"ieee":"M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum Markov semigroups,” <i>Annales Henri Poincare</i>, vol. 24. Springer Nature, pp. 717–750, 2023.","chicago":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00023-022-01220-x\">https://doi.org/10.1007/s00023-022-01220-x</a>.","ama":"Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov semigroups. <i>Annales Henri Poincare</i>. 2023;24:717-750. doi:<a href=\"https://doi.org/10.1007/s00023-022-01220-x\">10.1007/s00023-022-01220-x</a>","mla":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>, vol. 24, Springer Nature, 2023, pp. 717–50, doi:<a href=\"https://doi.org/10.1007/s00023-022-01220-x\">10.1007/s00023-022-01220-x</a>.","ista":"Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 24, 717–750.","short":"M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.","apa":"Wirth, M., &#38; Zhang, H. (2023). Curvature-dimension conditions for symmetric quantum Markov semigroups. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01220-x\">https://doi.org/10.1007/s00023-022-01220-x</a>"},"publication":"Annales Henri Poincare","external_id":{"isi":["000837499800002"],"arxiv":["2105.08303"]},"title":"Curvature-dimension conditions for symmetric quantum Markov semigroups","file":[{"creator":"dernst","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_name":"2023_AnnalesHenriPoincare_Wirth.pdf","file_size":554871,"checksum":"8c7b185eba5ccd92ef55c120f654222c","date_created":"2023-08-14T11:38:28Z","file_id":"14051","success":1,"date_updated":"2023-08-14T11:38:28Z"}],"status":"public","date_updated":"2023-08-14T11:39:28Z","publication_status":"published","page":"717-750","oa_version":"Published Version","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","ec_funded":1,"abstract":[{"text":"Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups.","lang":"eng"}]},{"publication_identifier":{"eissn":["1424-3202"],"issn":["1424-3199"]},"quality_controlled":"1","month":"01","volume":23,"article_type":"original","isi":1,"acknowledgement":"Research supported by the Austrian Science Fund (FWF) grant F65 at the Institute of Science and Technology Austria and by the European Research Council (ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 156).","department":[{"_id":"JaMa"}],"date_created":"2023-01-08T23:00:53Z","article_number":"9","intvolume":"        23","file_date_updated":"2023-01-20T10:45:06Z","article_processing_charge":"Yes (via OA deal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["510"],"_id":"12104","oa":1,"author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","first_name":"Melchior"}],"date_published":"2023-01-01T00:00:00Z","year":"2023","publisher":"Springer Nature","doi":"10.1007/s00028-022-00859-7","language":[{"iso":"eng"}],"type":"journal_article","title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","file":[{"creator":"dernst","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","file_size":422612,"file_id":"12325","date_created":"2023-01-20T10:45:06Z","checksum":"1f34f3e2cb521033de6154f274ea3a4e","date_updated":"2023-01-20T10:45:06Z","success":1}],"external_id":{"isi":["000906214600004"]},"publication":"Journal of Evolution Equations","citation":{"ieee":"L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms under order isomorphisms,” <i>Journal of Evolution Equations</i>, vol. 23, no. 1. Springer Nature, 2023.","chicago":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>.","ama":"Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. 2023;23(1). doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","apa":"Dello Schiavo, L., &#38; Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>","mla":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>, vol. 23, no. 1, 9, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>.","short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023)."},"project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020"},{"grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"},{"grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups"}],"has_accepted_license":"1","scopus_import":"1","issue":"1","abstract":[{"text":"We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces.","lang":"eng"}],"ec_funded":1,"day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication_status":"published","oa_version":"Published Version","date_updated":"2023-06-28T11:54:35Z","status":"public"},{"type":"journal_article","publisher":"Oxford University Press","year":"2023","language":[{"iso":"eng"}],"doi":"10.1093/evlett/qrac004","date_published":"2023-02-01T00:00:00Z","oa":1,"_id":"12521","author":[{"id":"353FAC84-AE61-11E9-8BFC-00D3E5697425","last_name":"Mrnjavac","first_name":"Andrea","full_name":"Mrnjavac, Andrea"},{"first_name":"Kseniia","full_name":"Khudiakova, Kseniia","last_name":"Khudiakova","id":"4E6DC800-AE37-11E9-AC72-31CAE5697425","orcid":"0000-0002-6246-1465"},{"id":"4880FE40-F248-11E8-B48F-1D18A9856A87","last_name":"Barton","orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H","first_name":"Nicholas H"},{"first_name":"Beatriz","full_name":"Vicoso, Beatriz","orcid":"0000-0002-4579-8306","id":"49E1C5C6-F248-11E8-B48F-1D18A9856A87","last_name":"Vicoso"}],"keyword":["Genetics","Ecology","Evolution","Behavior and Systematics"],"intvolume":"         7","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","ddc":["570"],"file_date_updated":"2023-08-16T11:43:33Z","pmid":1,"department":[{"_id":"GradSch"},{"_id":"BeVi"}],"acknowledgement":"We thank the Vicoso and Barton groups and ISTA Scientific Computing Unit. We also thank two anonymous reviewers for their valuable comments. This work was supported by the European Research Council under the European Union’s Horizon 2020 research and innovation program (grant agreements no. 715257 and no. 716117).","date_created":"2023-02-06T13:59:12Z","article_number":"qrac004","article_type":"original","volume":7,"isi":1,"quality_controlled":"1","publication_identifier":{"issn":["2056-3744"]},"month":"02","status":"public","date_updated":"2023-08-16T11:44:32Z","ec_funded":1,"abstract":[{"lang":"eng","text":"Differentiated X chromosomes are expected to have higher rates of adaptive divergence than autosomes, if new beneficial mutations are recessive (the “faster-X effect”), largely because these mutations are immediately exposed to selection in males. The evolution of X chromosomes after they stop recombining in males, but before they become hemizygous, has not been well explored theoretically. We use the diffusion approximation to infer substitution rates of beneficial and deleterious mutations under such a scenario. Our results show that selection is less efficient on diploid X loci than on autosomal and hemizygous X loci under a wide range of parameters. This “slower-X” effect is stronger for genes affecting primarily (or only) male fitness, and for sexually antagonistic genes. These unusual dynamics suggest that some of the peculiar features of X chromosomes, such as the differential accumulation of genes with sex-specific functions, may start arising earlier than previously appreciated."}],"oa_version":"Published Version","publication_status":"published","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"has_accepted_license":"1","issue":"1","scopus_import":"1","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020"},{"name":"Prevalence and Influence of Sexual Antagonism on Genome Evolution","_id":"250BDE62-B435-11E9-9278-68D0E5697425","grant_number":"715257","call_identifier":"H2020"}],"citation":{"ama":"Mrnjavac A, Khudiakova K, Barton NH, Vicoso B. Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution. <i>Evolution Letters</i>. 2023;7(1). doi:<a href=\"https://doi.org/10.1093/evlett/qrac004\">10.1093/evlett/qrac004</a>","ista":"Mrnjavac A, Khudiakova K, Barton NH, Vicoso B. 2023. Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution. Evolution Letters. 7(1), qrac004.","apa":"Mrnjavac, A., Khudiakova, K., Barton, N. H., &#38; Vicoso, B. (2023). Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution. <i>Evolution Letters</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/evlett/qrac004\">https://doi.org/10.1093/evlett/qrac004</a>","mla":"Mrnjavac, Andrea, et al. “Slower-X: Reduced Efficiency of Selection in the Early Stages of X Chromosome Evolution.” <i>Evolution Letters</i>, vol. 7, no. 1, qrac004, Oxford University Press, 2023, doi:<a href=\"https://doi.org/10.1093/evlett/qrac004\">10.1093/evlett/qrac004</a>.","short":"A. Mrnjavac, K. Khudiakova, N.H. Barton, B. Vicoso, Evolution Letters 7 (2023).","ieee":"A. Mrnjavac, K. Khudiakova, N. H. Barton, and B. Vicoso, “Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution,” <i>Evolution Letters</i>, vol. 7, no. 1. Oxford University Press, 2023.","chicago":"Mrnjavac, Andrea, Kseniia Khudiakova, Nicholas H Barton, and Beatriz Vicoso. “Slower-X: Reduced Efficiency of Selection in the Early Stages of X Chromosome Evolution.” <i>Evolution Letters</i>. Oxford University Press, 2023. <a href=\"https://doi.org/10.1093/evlett/qrac004\">https://doi.org/10.1093/evlett/qrac004</a>."},"external_id":{"pmid":["37065438"],"isi":["001021692200001"]},"title":"Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution","file":[{"file_size":2592189,"file_name":"2023_EvLetters_Mrnjavac.pdf","date_updated":"2023-08-16T11:43:33Z","success":1,"checksum":"a240a041cb9b9b7c8ba93a4706674a3f","date_created":"2023-08-16T11:43:33Z","file_id":"14068","creator":"dernst","relation":"main_file","content_type":"application/pdf","access_level":"open_access"}],"publication":"Evolution Letters"},{"date_published":"2023-08-15T00:00:00Z","_id":"12911","oa":1,"author":[{"full_name":"Feliciangeli, Dario","first_name":"Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Gerolin, Augusto","first_name":"Augusto","last_name":"Gerolin"},{"last_name":"Portinale","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo","full_name":"Portinale, Lorenzo"}],"type":"journal_article","year":"2023","publisher":"Elsevier","doi":"10.1016/j.jfa.2023.109963","language":[{"iso":"eng"}],"volume":285,"article_type":"original","isi":1,"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"quality_controlled":"1","month":"08","intvolume":"       285","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","acknowledgement":"This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813.","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"date_created":"2023-05-07T22:01:02Z","article_number":"109963","abstract":[{"text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.","lang":"eng"}],"ec_funded":1,"day":"15","publication_status":"published","oa_version":"Preprint","status":"public","date_updated":"2023-11-14T13:21:01Z","title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","external_id":{"arxiv":["2106.11217"],"isi":["000990804300001"]},"related_material":{"record":[{"id":"9792","status":"public","relation":"earlier_version"}]},"publication":"Journal of Functional Analysis","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"scopus_import":"1","issue":"4","citation":{"ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>Journal of Functional Analysis</i>. 2023;285(4). doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">10.1016/j.jfa.2023.109963</a>","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional Analysis</i>, vol. 285, no. 4, 109963, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">10.1016/j.jfa.2023.109963</a>.","short":"D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023).","apa":"Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">https://doi.org/10.1016/j.jfa.2023.109963</a>","ista":"Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 285(4), 109963.","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” <i>Journal of Functional Analysis</i>, vol. 285, no. 4. Elsevier, 2023.","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">https://doi.org/10.1016/j.jfa.2023.109963</a>."},"arxiv":1,"project":[{"grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"grant_number":" F06504","call_identifier":"FWF","name":"Taming Complexity in Partial Di erential Systems","_id":"260482E2-B435-11E9-9278-68D0E5697425"}]},{"date_updated":"2023-10-04T11:34:49Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"28","oa_version":"Published Version","publication_status":"published","abstract":[{"text":"This paper deals with the large-scale behaviour of dynamical optimal transport on Zd\r\n-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes the effective behaviour of the discrete problems in terms of a continuous optimal transport problem. The effective energy density can be explicitly expressed in terms of a cell formula, which is a finite-dimensional convex programming problem that depends non-trivially on the local geometry of the discrete graph and the discrete energy density. Our homogenisation result is derived from a Γ\r\n-convergence result for action functionals on curves of measures, which we prove under very mild growth conditions on the energy density. We investigate the cell formula in several cases of interest, including finite-volume discretisations of the Wasserstein distance, where non-trivial limiting behaviour occurs.","lang":"eng"}],"ec_funded":1,"citation":{"ista":"Gladbach P, Kopfer E, Maas J, Portinale L. 2023. Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. 62(5), 143.","mla":"Gladbach, Peter, et al. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 62, no. 5, 143, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00526-023-02472-z\">10.1007/s00526-023-02472-z</a>.","short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and Partial Differential Equations 62 (2023).","apa":"Gladbach, P., Kopfer, E., Maas, J., &#38; Portinale, L. (2023). Homogenisation of dynamical optimal transport on periodic graphs. <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00526-023-02472-z\">https://doi.org/10.1007/s00526-023-02472-z</a>","ama":"Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of dynamical optimal transport on periodic graphs. <i>Calculus of Variations and Partial Differential Equations</i>. 2023;62(5). doi:<a href=\"https://doi.org/10.1007/s00526-023-02472-z\">10.1007/s00526-023-02472-z</a>","chicago":"Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00526-023-02472-z\">https://doi.org/10.1007/s00526-023-02472-z</a>.","ieee":"P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of dynamical optimal transport on periodic graphs,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 62, no. 5. Springer Nature, 2023."},"arxiv":1,"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","_id":"260788DE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"scopus_import":"1","issue":"5","has_accepted_license":"1","publication":"Calculus of Variations and Partial Differential Equations","file":[{"checksum":"359bee38d94b7e0aa73925063cb8884d","date_created":"2023-10-04T11:34:10Z","file_id":"14393","date_updated":"2023-10-04T11:34:10Z","success":1,"file_name":"2023_CalculusEquations_Gladbach.pdf","file_size":1240995,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","creator":"dernst"}],"title":"Homogenisation of dynamical optimal transport on periodic graphs","external_id":{"arxiv":["2110.15321"],"isi":["000980588900001"]},"doi":"10.1007/s00526-023-02472-z","language":[{"iso":"eng"}],"year":"2023","publisher":"Springer Nature","type":"journal_article","author":[{"last_name":"Gladbach","full_name":"Gladbach, Peter","first_name":"Peter"},{"full_name":"Kopfer, Eva","first_name":"Eva","last_name":"Kopfer"},{"orcid":"0000-0002-0845-1338","last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","first_name":"Jan"},{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale","full_name":"Portinale, Lorenzo","first_name":"Lorenzo"}],"_id":"12959","oa":1,"date_published":"2023-04-28T00:00:00Z","date_created":"2023-05-14T22:01:00Z","article_number":"143","acknowledgement":"J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117). J.M and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—350398276. We thank the anonymous reviewer for the careful reading and for useful suggestions. Open access funding provided by Austrian Science Fund (FWF).","department":[{"_id":"JaMa"}],"file_date_updated":"2023-10-04T11:34:10Z","ddc":["510"],"article_processing_charge":"Yes (via OA deal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        62","month":"04","publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"quality_controlled":"1","isi":1,"article_type":"original","volume":62},{"external_id":{"isi":["000780305000001"]},"file":[{"file_name":"2022_JourStatisticalPhysics_Wirth.pdf","file_size":362119,"date_created":"2022-04-29T11:24:23Z","checksum":"f3e0b00884b7dde31347a3756788b473","file_id":"11338","date_updated":"2022-04-29T11:24:23Z","success":1,"creator":"dernst","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"title":"A dual formula for the noncommutative transport distance","publication":"Journal of Statistical Physics","has_accepted_license":"1","issue":"2","scopus_import":"1","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"citation":{"ista":"Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19.","apa":"Wirth, M. (2022). A dual formula for the noncommutative transport distance. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-022-02911-9\">https://doi.org/10.1007/s10955-022-02911-9</a>","short":"M. Wirth, Journal of Statistical Physics 187 (2022).","mla":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” <i>Journal of Statistical Physics</i>, vol. 187, no. 2, 19, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02911-9\">10.1007/s10955-022-02911-9</a>.","ama":"Wirth M. A dual formula for the noncommutative transport distance. <i>Journal of Statistical Physics</i>. 2022;187(2). doi:<a href=\"https://doi.org/10.1007/s10955-022-02911-9\">10.1007/s10955-022-02911-9</a>","chicago":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-022-02911-9\">https://doi.org/10.1007/s10955-022-02911-9</a>.","ieee":"M. Wirth, “A dual formula for the noncommutative transport distance,” <i>Journal of Statistical Physics</i>, vol. 187, no. 2. Springer Nature, 2022."},"ec_funded":1,"abstract":[{"lang":"eng","text":"In this article we study the noncommutative transport distance introduced by Carlen and Maas and its entropic regularization defined by Becker and Li. We prove a duality formula that can be understood as a quantum version of the dual Benamou–Brenier formulation of the Wasserstein distance in terms of subsolutions of a Hamilton–Jacobi–Bellmann equation."}],"oa_version":"Published Version","publication_status":"published","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"08","status":"public","date_updated":"2023-08-03T06:37:49Z","article_type":"original","volume":187,"isi":1,"quality_controlled":"1","publication_identifier":{"issn":["00224715"],"eissn":["15729613"]},"month":"04","intvolume":"       187","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","ddc":["510","530"],"file_date_updated":"2022-04-29T11:24:23Z","acknowledgement":"The author wants to thank Jan Maas for helpful comments. He also acknowledges financial support from the Austrian Science Fund (FWF) through Grant Number F65 and from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No. 716117).\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","department":[{"_id":"JaMa"}],"article_number":"19","date_created":"2022-04-24T22:01:43Z","date_published":"2022-04-08T00:00:00Z","oa":1,"_id":"11330","author":[{"first_name":"Melchior","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"type":"journal_article","publisher":"Springer Nature","year":"2022","language":[{"iso":"eng"}],"doi":"10.1007/s10955-022-02911-9"},{"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"}],"arxiv":1,"citation":{"ama":"Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. <i>Annals of Probability</i>. 2022;50(2):591-648. doi:<a href=\"https://doi.org/10.1214/21-AOP1541\">10.1214/21-AOP1541</a>","short":"L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.","ista":"Dello Schiavo L. 2022. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. 50(2), 591–648.","mla":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” <i>Annals of Probability</i>, vol. 50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:<a href=\"https://doi.org/10.1214/21-AOP1541\">10.1214/21-AOP1541</a>.","apa":"Dello Schiavo, L. (2022). The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AOP1541\">https://doi.org/10.1214/21-AOP1541</a>","ieee":"L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold,” <i>Annals of Probability</i>, vol. 50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.","chicago":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AOP1541\">https://doi.org/10.1214/21-AOP1541</a>."},"issue":"2","scopus_import":"1","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.1811.11598"}],"publication":"Annals of Probability","external_id":{"isi":["000773518500005"],"arxiv":["1811.11598"]},"title":"The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold","date_updated":"2023-10-17T12:50:24Z","status":"public","publication_status":"published","oa_version":"Preprint","page":"591-648","day":"01","ec_funded":1,"abstract":[{"lang":"eng","text":"We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics."}],"date_created":"2022-05-08T22:01:44Z","department":[{"_id":"JaMa"}],"acknowledgement":"Research supported by the Sonderforschungsbereich 1060 and the Hausdorff Center for Mathematics. The author gratefully acknowledges funding of his current position at IST Austria by the Austrian Science Fund (FWF) grant F65 and by the European Research Council (ERC, Grant agreement No. 716117, awarded to Prof. Dr. Jan Maas).","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        50","month":"03","quality_controlled":"1","publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"isi":1,"volume":50,"article_type":"original","language":[{"iso":"eng"}],"doi":"10.1214/21-AOP1541","publisher":"Institute of Mathematical Statistics","year":"2022","type":"journal_article","author":[{"first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870"}],"oa":1,"_id":"11354","date_published":"2022-03-01T00:00:00Z"},{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.05677","open_access":"1"}],"title":"Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph","external_id":{"arxiv":["2105.05677"],"isi":["000812422100001"]},"publication":"Networks and Heterogeneous Media","arxiv":1,"citation":{"ieee":"M. Erbar, D. L. Forkert, J. Maas, and D. Mugnolo, “Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph,” <i>Networks and Heterogeneous Media</i>, vol. 17, no. 5. American Institute of Mathematical Sciences, pp. 687–717, 2022.","chicago":"Erbar, Matthias, Dominik L Forkert, Jan Maas, and Delio Mugnolo. “Gradient Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric Graph.” <i>Networks and Heterogeneous Media</i>. American Institute of Mathematical Sciences, 2022. <a href=\"https://doi.org/10.3934/nhm.2022023\">https://doi.org/10.3934/nhm.2022023</a>.","ama":"Erbar M, Forkert DL, Maas J, Mugnolo D. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. <i>Networks and Heterogeneous Media</i>. 2022;17(5):687-717. doi:<a href=\"https://doi.org/10.3934/nhm.2022023\">10.3934/nhm.2022023</a>","short":"M. Erbar, D.L. Forkert, J. Maas, D. Mugnolo, Networks and Heterogeneous Media 17 (2022) 687–717.","apa":"Erbar, M., Forkert, D. L., Maas, J., &#38; Mugnolo, D. (2022). Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. <i>Networks and Heterogeneous Media</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/nhm.2022023\">https://doi.org/10.3934/nhm.2022023</a>","ista":"Erbar M, Forkert DL, Maas J, Mugnolo D. 2022. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media. 17(5), 687–717.","mla":"Erbar, Matthias, et al. “Gradient Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric Graph.” <i>Networks and Heterogeneous Media</i>, vol. 17, no. 5, American Institute of Mathematical Sciences, 2022, pp. 687–717, doi:<a href=\"https://doi.org/10.3934/nhm.2022023\">10.3934/nhm.2022023</a>."},"project":[{"call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"scopus_import":"1","issue":"5","abstract":[{"lang":"eng","text":"This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou–Brenier formula for the Wasserstein distance, which establishes the equivalence of static and dynamical optimal transport. Secondly, in the spirit of Jordan–Kinderlehrer–Otto, we show that McKean–Vlasov equations can be formulated as gradient flow of the free energy in the Wasserstein space of probability measures. The proofs of these results are based on careful regularisation arguments to circumvent some of the difficulties arising in metric graphs, namely, branching of geodesics and the failure of semi-convexity of entropy functionals in the Wasserstein space."}],"ec_funded":1,"day":"01","publication_status":"published","page":"687-717","oa_version":"Preprint","date_updated":"2023-08-03T12:25:49Z","status":"public","publication_identifier":{"eissn":["1556-181X"],"issn":["1556-1801"]},"quality_controlled":"1","month":"10","volume":17,"article_type":"original","isi":1,"acknowledgement":"ME acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG), Grant SFB 1283/2 2021 – 317210226. DF and JM were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117). JM also acknowledges support by the Austrian Science Fund (FWF), Project SFB F65. The work of DM was partially supported by the Deutsche Forschungsgemeinschaft\r\n(DFG), Grant 397230547. This article is based upon work from COST Action\r\n18232 MAT-DYN-NET, supported by COST (European Cooperation in Science\r\nand Technology), www.cost.eu. We wish to thank Martin Burger and Jan-Frederik\r\nPietschmann for useful discussions. We are grateful to the anonymous referees for\r\ntheir careful reading and useful suggestions.","department":[{"_id":"JaMa"}],"date_created":"2022-07-31T22:01:46Z","intvolume":"        17","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"11700","oa":1,"author":[{"full_name":"Erbar, Matthias","first_name":"Matthias","last_name":"Erbar"},{"id":"35C79D68-F248-11E8-B48F-1D18A9856A87","last_name":"Forkert","full_name":"Forkert, Dominik L","first_name":"Dominik L"},{"first_name":"Jan","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas"},{"last_name":"Mugnolo","full_name":"Mugnolo, Delio","first_name":"Delio"}],"date_published":"2022-10-01T00:00:00Z","year":"2022","publisher":"American Institute of Mathematical Sciences","doi":"10.3934/nhm.2022023","language":[{"iso":"eng"}],"type":"journal_article"},{"doi":"10.1137/21M1410968","language":[{"iso":"eng"}],"year":"2022","publisher":"Society for Industrial and Applied Mathematics","type":"journal_article","author":[{"last_name":"Forkert","id":"35C79D68-F248-11E8-B48F-1D18A9856A87","full_name":"Forkert, Dominik L","first_name":"Dominik L"},{"full_name":"Maas, Jan","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","orcid":"0000-0002-0845-1338"},{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale","first_name":"Lorenzo","full_name":"Portinale, Lorenzo"}],"_id":"11739","oa":1,"date_published":"2022-07-18T00:00:00Z","date_created":"2022-08-07T22:01:59Z","department":[{"_id":"JaMa"}],"acknowledgement":"This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme grant 716117 and by the AustrianScience Fund (FWF) through grants F65 and W1245.","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"        54","keyword":["Fokker--Planck equation","gradient flow","evolutionary $\\Gamma$-convergence"],"month":"07","publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"quality_controlled":"1","isi":1,"volume":54,"article_type":"original","date_updated":"2023-08-03T12:37:21Z","status":"public","day":"18","page":"4297-4333","publication_status":"published","oa_version":"Preprint","abstract":[{"text":"We consider finite-volume approximations of Fokker--Planck equations on bounded convex domains in $\\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker--Planck equation via the method of evolutionary $\\Gamma$-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalizing the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality.","lang":"eng"}],"ec_funded":1,"citation":{"mla":"Forkert, Dominik L., et al. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 4297–333, doi:<a href=\"https://doi.org/10.1137/21M1410968\">10.1137/21M1410968</a>.","apa":"Forkert, D. L., Maas, J., &#38; Portinale, L. (2022). Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21M1410968\">https://doi.org/10.1137/21M1410968</a>","ista":"Forkert DL, Maas J, Portinale L. 2022. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. 54(4), 4297–4333.","short":"D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis 54 (2022) 4297–4333.","ama":"Forkert DL, Maas J, Portinale L. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. <i>SIAM Journal on Mathematical Analysis</i>. 2022;54(4):4297-4333. doi:<a href=\"https://doi.org/10.1137/21M1410968\">10.1137/21M1410968</a>","chicago":"Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21M1410968\">https://doi.org/10.1137/21M1410968</a>.","ieee":"D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 4. Society for Industrial and Applied Mathematics, pp. 4297–4333, 2022."},"arxiv":1,"project":[{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","_id":"260788DE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"scopus_import":"1","issue":"4","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2008.10962"}],"publication":"SIAM Journal on Mathematical Analysis","title":"Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions","external_id":{"isi":["000889274600001"],"arxiv":["2008.10962"]},"related_material":{"record":[{"status":"public","id":"10022","relation":"earlier_version"}]}},{"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s00208-021-02331-2","publisher":"Springer Nature","year":"2022","date_published":"2022-12-01T00:00:00Z","author":[{"last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo"},{"last_name":"Suzuki","first_name":"Kohei","full_name":"Suzuki, Kohei"}],"oa":1,"_id":"10588","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["510"],"article_processing_charge":"Yes (via OA deal)","file_date_updated":"2022-01-03T11:08:31Z","keyword":["quasi curvature-dimension condition","sub-riemannian geometry","Sobolev-to-Lipschitz property","Varadhan short-time asymptotics"],"intvolume":"       384","date_created":"2022-01-02T23:01:35Z","acknowledgement":"The authors are grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino Antonelli for reading a preliminary version of this work and for their valuable comments and suggestions. Finally, they wish to express their gratitude to two anonymous Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S. gratefully acknowledges funding of his position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium.","department":[{"_id":"JaMa"}],"isi":1,"volume":384,"article_type":"original","month":"12","quality_controlled":"1","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"status":"public","date_updated":"2023-08-02T13:39:05Z","page":"1815-1832","publication_status":"published","oa_version":"Published Version","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ec_funded":1,"abstract":[{"lang":"eng","text":"We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds."}],"scopus_import":"1","has_accepted_license":"1","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"citation":{"ieee":"L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces and applications,” <i>Mathematische Annalen</i>, vol. 384. Springer Nature, pp. 1815–1832, 2022.","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” <i>Mathematische Annalen</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00208-021-02331-2\">https://doi.org/10.1007/s00208-021-02331-2</a>.","ama":"Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and applications. <i>Mathematische Annalen</i>. 2022;384:1815-1832. doi:<a href=\"https://doi.org/10.1007/s00208-021-02331-2\">10.1007/s00208-021-02331-2</a>","ista":"Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 384, 1815–1832.","apa":"Dello Schiavo, L., &#38; Suzuki, K. (2022). Sobolev-to-Lipschitz property on QCD- spaces and applications. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-021-02331-2\">https://doi.org/10.1007/s00208-021-02331-2</a>","short":"L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” <i>Mathematische Annalen</i>, vol. 384, Springer Nature, 2022, pp. 1815–32, doi:<a href=\"https://doi.org/10.1007/s00208-021-02331-2\">10.1007/s00208-021-02331-2</a>."},"arxiv":1,"publication":"Mathematische Annalen","external_id":{"arxiv":["2110.05137"],"isi":["000734150200001"]},"title":"Sobolev-to-Lipschitz property on QCD- spaces and applications","file":[{"file_size":410090,"file_name":"2021_MathAnn_DelloSchiavo.pdf","date_updated":"2022-01-03T11:08:31Z","success":1,"date_created":"2022-01-03T11:08:31Z","file_id":"10596","checksum":"2593abbf195e38efa93b6006b1e90eb1","creator":"alisjak","relation":"main_file","content_type":"application/pdf","access_level":"open_access"}]},{"publication":"Proceedings of the American Mathematical Society, Series B","file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","creator":"dernst","file_id":"12404","checksum":"cb4a79937c1f60d4c329a10ee797f0d2","date_created":"2023-01-26T13:02:07Z","date_updated":"2023-01-26T13:02:07Z","success":1,"file_name":"2022_ProceedingsAMS_Cremaschi.pdf","file_size":326471}],"title":"Effective contraction of Skinning maps","citation":{"ama":"Cremaschi T, Dello Schiavo L. Effective contraction of Skinning maps. <i>Proceedings of the American Mathematical Society, Series B</i>. 2022;9(43):445-459. doi:<a href=\"https://doi.org/10.1090/bproc/134\">10.1090/bproc/134</a>","apa":"Cremaschi, T., &#38; Dello Schiavo, L. (2022). Effective contraction of Skinning maps. <i>Proceedings of the American Mathematical Society, Series B</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/bproc/134\">https://doi.org/10.1090/bproc/134</a>","ista":"Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 9(43), 445–459.","mla":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” <i>Proceedings of the American Mathematical Society, Series B</i>, vol. 9, no. 43, American Mathematical Society, 2022, pp. 445–59, doi:<a href=\"https://doi.org/10.1090/bproc/134\">10.1090/bproc/134</a>.","short":"T. Cremaschi, L. Dello Schiavo, Proceedings of the American Mathematical Society, Series B 9 (2022) 445–459.","ieee":"T. Cremaschi and L. Dello Schiavo, “Effective contraction of Skinning maps,” <i>Proceedings of the American Mathematical Society, Series B</i>, vol. 9, no. 43. American Mathematical Society, pp. 445–459, 2022.","chicago":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” <i>Proceedings of the American Mathematical Society, Series B</i>. American Mathematical Society, 2022. <a href=\"https://doi.org/10.1090/bproc/134\">https://doi.org/10.1090/bproc/134</a>."},"project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"}],"scopus_import":"1","issue":"43","has_accepted_license":"1","day":"02","tmp":{"image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"oa_version":"Published Version","page":"445-459","publication_status":"published","abstract":[{"lang":"eng","text":"Using elementary hyperbolic geometry, we give an explicit formula for the contraction constant of the skinning map over moduli spaces of relatively acylindrical hyperbolic manifolds."}],"ec_funded":1,"date_updated":"2023-01-26T13:04:13Z","status":"public","month":"11","publication_identifier":{"issn":["2330-1511"]},"quality_controlled":"1","volume":9,"article_type":"original","date_created":"2023-01-12T12:12:17Z","department":[{"_id":"JaMa"}],"acknowledgement":"The first author was partially supported by the National Science Foundation under Grant\r\nNo. DMS-1928930 while participating in a program hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2020 semester. The second author gratefully acknowledges funding by the Austrian Science Fund (FWF) through grants F65 and ESPRIT 208, by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas), and by the Deutsche Forschungsgemeinschaft through the SPP 2265.","file_date_updated":"2023-01-26T13:02:07Z","article_processing_charge":"No","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"         9","author":[{"first_name":"Tommaso","full_name":"Cremaschi, Tommaso","last_name":"Cremaschi"},{"last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo"}],"_id":"12177","oa":1,"date_published":"2022-11-02T00:00:00Z","doi":"10.1090/bproc/134","language":[{"iso":"eng"}],"year":"2022","publisher":"American Mathematical Society","type":"journal_article"},{"author":[{"last_name":"Karatzas","first_name":"Ioannis","full_name":"Karatzas, Ioannis"},{"last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338","first_name":"Jan","full_name":"Maas, Jan"},{"last_name":"Schachermayer","first_name":"Walter","full_name":"Schachermayer, Walter"}],"_id":"10023","oa":1,"date_published":"2021-06-04T00:00:00Z","doi":"10.4310/CIS.2021.v21.n4.a1","language":[{"iso":"eng"}],"year":"2021","publisher":"International Press","type":"journal_article","month":"06","publication_identifier":{"issn":["1526-7555"]},"quality_controlled":"1","volume":21,"article_type":"original","date_created":"2021-09-19T08:53:19Z","department":[{"_id":"JaMa"}],"acknowledgement":"I.K. acknowledges support from the U.S. National Science Foundation under Grant NSF-DMS-20-04997. J.M. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117) and from the Austrian Science Fund (FWF) through project F65. W.S. acknowledges support from the Austrian Science Fund (FWF) under grant P28861 and by the Vienna Science and Technology Fund (WWTF) through projects MA14-008 and MA16-021.","article_processing_charge":"No","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","intvolume":"        21","keyword":["Markov Chain","relative entropy","time reversal","steepest descent","gradient flow"],"day":"04","oa_version":"Preprint","page":"481-536","publication_status":"published","abstract":[{"lang":"eng","text":"We study the temporal dissipation of variance and relative entropy for ergodic Markov Chains in continuous time, and compute explicitly the corresponding dissipation rates. These are identified, as is well known, in the case of the variance in terms of an appropriate Hilbertian norm; and in the case of the relative entropy, in terms of a Dirichlet form which morphs into a version of the familiar Fisher information under conditions of detailed balance. Here we obtain trajectorial versions of these results, valid along almost every path of the random motion and most transparent in the backwards direction of time. Martingale arguments and time reversal play crucial roles, as in the recent work of Karatzas, Schachermayer and Tschiderer for conservative diffusions. Extensions are developed to general “convex divergences” and to countable state-spaces. The steepest descent and gradient flow properties for the variance, the relative entropy, and appropriate generalizations, are studied along with their respective geometries under conditions of detailed balance, leading to a very direct proof for the HWI inequality of Otto and Villani in the present context."}],"ec_funded":1,"date_updated":"2021-09-20T12:51:18Z","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2005.14177"}],"publication":"Communications in Information and Systems","title":"Trajectorial dissipation and gradient flow for the relative entropy in Markov chains","external_id":{"arxiv":["2005.14177"]},"citation":{"mla":"Karatzas, Ioannis, et al. “Trajectorial Dissipation and Gradient Flow for the Relative Entropy in Markov Chains.” <i>Communications in Information and Systems</i>, vol. 21, no. 4, International Press, 2021, pp. 481–536, doi:<a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">10.4310/CIS.2021.v21.n4.a1</a>.","short":"I. Karatzas, J. Maas, W. Schachermayer, Communications in Information and Systems 21 (2021) 481–536.","ista":"Karatzas I, Maas J, Schachermayer W. 2021. Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. Communications in Information and Systems. 21(4), 481–536.","apa":"Karatzas, I., Maas, J., &#38; Schachermayer, W. (2021). Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. <i>Communications in Information and Systems</i>. International Press. <a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">https://doi.org/10.4310/CIS.2021.v21.n4.a1</a>","ama":"Karatzas I, Maas J, Schachermayer W. Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. <i>Communications in Information and Systems</i>. 2021;21(4):481-536. doi:<a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">10.4310/CIS.2021.v21.n4.a1</a>","chicago":"Karatzas, Ioannis, Jan Maas, and Walter Schachermayer. “Trajectorial Dissipation and Gradient Flow for the Relative Entropy in Markov Chains.” <i>Communications in Information and Systems</i>. International Press, 2021. <a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">https://doi.org/10.4310/CIS.2021.v21.n4.a1</a>.","ieee":"I. Karatzas, J. Maas, and W. Schachermayer, “Trajectorial dissipation and gradient flow for the relative entropy in Markov chains,” <i>Communications in Information and Systems</i>, vol. 21, no. 4. International Press, pp. 481–536, 2021."},"arxiv":1,"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"issue":"4"},{"author":[{"orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo"},{"last_name":"Suzuki","full_name":"Suzuki, Kohei","first_name":"Kohei"}],"oa":1,"_id":"10070","date_published":"2021-09-15T00:00:00Z","language":[{"iso":"eng"}],"doi":"10.1016/j.jfa.2021.109234","publisher":"Elsevier","year":"2021","type":"journal_article","month":"09","quality_controlled":"1","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"isi":1,"article_type":"original","volume":281,"article_number":"109234","date_created":"2021-10-03T22:01:21Z","acknowledgement":"The authors are grateful to Professor Kazuhiro Kuwae for kindly providing a copy of [49]. They are also grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces. They wish to express their deepest gratitude to an anonymous Reviewer, whose punctual remarks and comments greatly improved the accessibility and overall quality of the initial submission. This work was completed while L.D.S. was a member of the Institut für Angewandte Mathematik of the University of Bonn. He acknowledges funding of his position at that time by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Sonderforschungsbereich (Sfb, Collaborative Research Center) 1060 - project number 211504053. He also acknowledges funding of his current position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas). K.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; and JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465.","department":[{"_id":"JaMa"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","intvolume":"       281","publication_status":"published","oa_version":"Preprint","day":"15","ec_funded":1,"abstract":[{"lang":"eng","text":"We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As an application, we prove the integral Varadhan short-time asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms."}],"date_updated":"2023-08-14T07:05:44Z","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2008.01492"}],"publication":"Journal of Functional Analysis","external_id":{"isi":["000703896600005"],"arxiv":["2008.01492"]},"title":"Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"}],"citation":{"ama":"Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>. 2021;281(11). doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">10.1016/j.jfa.2021.109234</a>","apa":"Dello Schiavo, L., &#38; Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">https://doi.org/10.1016/j.jfa.2021.109234</a>","ista":"Dello Schiavo L, Suzuki K. 2021. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. 281(11), 109234.","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” <i>Journal of Functional Analysis</i>, vol. 281, no. 11, 109234, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">10.1016/j.jfa.2021.109234</a>.","short":"L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).","ieee":"L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces,” <i>Journal of Functional Analysis</i>, vol. 281, no. 11. Elsevier, 2021.","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">https://doi.org/10.1016/j.jfa.2021.109234</a>."},"arxiv":1,"issue":"11","scopus_import":"1"},{"publisher":"Institute of Science and Technology Austria","year":"2021","language":[{"iso":"eng"}],"doi":"10.15479/at:ista:9733","type":"dissertation","oa":1,"_id":"9733","author":[{"first_name":"Dario","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87"}],"date_published":"2021-08-20T00:00:00Z","department":[{"_id":"GradSch"},{"_id":"RoSe"},{"_id":"JaMa"}],"date_created":"2021-07-27T15:48:30Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["515","519","539"],"article_processing_charge":"No","file_date_updated":"2022-03-10T12:13:57Z","publication_identifier":{"issn":["2663-337X"]},"month":"08","supervisor":[{"orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert"},{"first_name":"Jan","full_name":"Maas, Jan","last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338"}],"date_updated":"2024-03-06T12:30:44Z","license":"https://creativecommons.org/licenses/by-nd/4.0/","status":"public","degree_awarded":"PhD","ec_funded":1,"abstract":[{"lang":"eng","text":"This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author."}],"oa_version":"Published Version","publication_status":"published","page":"180","tmp":{"short":"CC BY-ND (4.0)","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode"},"day":"20","project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"citation":{"ieee":"D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and Technology Austria, 2021.","chicago":"Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/at:ista:9733\">https://doi.org/10.15479/at:ista:9733</a>.","ama":"Feliciangeli D. The polaron at strong coupling. 2021. doi:<a href=\"https://doi.org/10.15479/at:ista:9733\">10.15479/at:ista:9733</a>","ista":"Feliciangeli D. 2021. The polaron at strong coupling. Institute of Science and Technology Austria.","mla":"Feliciangeli, Dario. <i>The Polaron at Strong Coupling</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/at:ista:9733\">10.15479/at:ista:9733</a>.","short":"D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and Technology Austria, 2021.","apa":"Feliciangeli, D. (2021). <i>The polaron at strong coupling</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:9733\">https://doi.org/10.15479/at:ista:9733</a>"},"alternative_title":["ISTA Thesis"],"has_accepted_license":"1","related_material":{"record":[{"status":"public","id":"9787","relation":"part_of_dissertation"},{"status":"public","id":"9792","relation":"part_of_dissertation"},{"status":"public","id":"9225","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"9781","status":"public"},{"status":"public","id":"9791","relation":"part_of_dissertation"}]},"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","creator":"dfelicia","date_updated":"2021-09-06T09:28:56Z","file_id":"9944","date_created":"2021-08-19T14:03:48Z","checksum":"e88bb8ca43948abe060eb2d2fa719881","file_size":1958710,"file_name":"Thesis_FeliciangeliA.pdf"},{"date_updated":"2022-03-10T12:13:57Z","file_id":"9945","checksum":"72810843abee83705853505b3f8348aa","date_created":"2021-08-19T14:06:35Z","file_size":3771669,"file_name":"thesis.7z","content_type":"application/octet-stream","relation":"source_file","access_level":"closed","creator":"dfelicia"}],"title":"The polaron at strong coupling"},{"month":"07","article_number":"2106.11217","date_created":"2021-08-06T09:07:12Z","acknowledgement":"This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thanks the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. Finally, the authors also thanks J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article.  L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and NoF65. D.F acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942].","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"article_processing_charge":"No","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","first_name":"Dario"},{"last_name":"Gerolin","first_name":"Augusto","full_name":"Gerolin, Augusto"},{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale","full_name":"Portinale, Lorenzo","first_name":"Lorenzo"}],"oa":1,"_id":"9792","date_published":"2021-07-21T00:00:00Z","language":[{"iso":"eng"}],"doi":"10.48550/arXiv.2106.11217","year":"2021","type":"preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2106.11217","open_access":"1"}],"publication":"arXiv","external_id":{"arxiv":["2106.11217"]},"related_material":{"record":[{"id":"9733","status":"public","relation":"dissertation_contains"},{"relation":"dissertation_contains","status":"public","id":"10030"},{"relation":"later_version","status":"public","id":"12911"}]},"title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","project":[{"grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"},{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"citation":{"ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” <i>arXiv</i>. .","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2106.11217\">https://doi.org/10.48550/arXiv.2106.11217</a>.","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2106.11217\">10.48550/arXiv.2106.11217</a>","ista":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv, 2106.11217.","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>ArXiv</i>, 2106.11217, doi:<a href=\"https://doi.org/10.48550/arXiv.2106.11217\">10.48550/arXiv.2106.11217</a>.","short":"D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.).","apa":"Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (n.d.). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2106.11217\">https://doi.org/10.48550/arXiv.2106.11217</a>"},"arxiv":1,"has_accepted_license":"1","publication_status":"submitted","oa_version":"Preprint","day":"21","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ec_funded":1,"abstract":[{"text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on careful a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.","lang":"eng"}],"date_updated":"2023-11-14T13:21:01Z","status":"public"},{"file_date_updated":"2021-02-04T10:29:11Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["510"],"article_processing_charge":"No","intvolume":"       181","date_created":"2020-11-15T23:01:18Z","acknowledgement":"The research of A.M. was partially supported by the Deutsche Forschungsgemeinschaft (DFG) via the Collaborative Research Center SFB 1114 Scaling Cascades in Complex Systems (Project No. 235221301), through the Subproject C05 Effective models for materials and interfaces with multiple scales. J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117), and by the Austrian Science Fund (FWF), Project SFB F65. The authors thank Christof Schütte, Robert I. A. Patterson, and Stefanie Winkelmann for helpful and stimulating discussions. Open access funding provided by Austrian Science Fund (FWF).","department":[{"_id":"JaMa"}],"isi":1,"article_type":"original","volume":181,"month":"12","publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"quality_controlled":"1","type":"journal_article","doi":"10.1007/s10955-020-02663-4","language":[{"iso":"eng"}],"year":"2020","publisher":"Springer Nature","date_published":"2020-12-01T00:00:00Z","author":[{"first_name":"Jan","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","orcid":"0000-0002-0845-1338"},{"first_name":"Alexander","full_name":"Mielke, Alexander","last_name":"Mielke"}],"_id":"8758","oa":1,"scopus_import":"1","issue":"6","has_accepted_license":"1","arxiv":1,"citation":{"ama":"Maas J, Mielke A. Modeling of chemical reaction systems with detailed balance using gradient structures. <i>Journal of Statistical Physics</i>. 2020;181(6):2257-2303. doi:<a href=\"https://doi.org/10.1007/s10955-020-02663-4\">10.1007/s10955-020-02663-4</a>","apa":"Maas, J., &#38; Mielke, A. (2020). Modeling of chemical reaction systems with detailed balance using gradient structures. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-020-02663-4\">https://doi.org/10.1007/s10955-020-02663-4</a>","ista":"Maas J, Mielke A. 2020. Modeling of chemical reaction systems with detailed balance using gradient structures. Journal of Statistical Physics. 181(6), 2257–2303.","short":"J. Maas, A. Mielke, Journal of Statistical Physics 181 (2020) 2257–2303.","mla":"Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” <i>Journal of Statistical Physics</i>, vol. 181, no. 6, Springer Nature, 2020, pp. 2257–303, doi:<a href=\"https://doi.org/10.1007/s10955-020-02663-4\">10.1007/s10955-020-02663-4</a>.","ieee":"J. Maas and A. Mielke, “Modeling of chemical reaction systems with detailed balance using gradient structures,” <i>Journal of Statistical Physics</i>, vol. 181, no. 6. Springer Nature, pp. 2257–2303, 2020.","chicago":"Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s10955-020-02663-4\">https://doi.org/10.1007/s10955-020-02663-4</a>."},"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020"},{"grant_number":" F06504","call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425","name":"Taming Complexity in Partial Di erential Systems"}],"publication":"Journal of Statistical Physics","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","creator":"dernst","success":1,"date_updated":"2021-02-04T10:29:11Z","file_id":"9087","date_created":"2021-02-04T10:29:11Z","checksum":"bc2b63a90197b97cbc73eccada4639f5","file_size":753596,"file_name":"2020_JourStatPhysics_Maas.pdf"}],"title":"Modeling of chemical reaction systems with detailed balance using gradient structures","external_id":{"arxiv":["2004.02831"],"isi":["000587107200002"]},"status":"public","date_updated":"2023-08-22T13:24:27Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","page":"2257-2303","publication_status":"published","oa_version":"Published Version","abstract":[{"text":"We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.","lang":"eng"}],"ec_funded":1},{"day":"21","publication_status":"published","oa_version":"Preprint","page":"1-27","abstract":[{"lang":"eng","text":"We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean  space,  motivated  by  the  famous  theorem  of  Gromov  about  the  waist  of  radially symmetric Gaussian measures.  In particular, it turns our possible to extend Gromov’s original result  to  the  case  of  not  necessarily  radially  symmetric  Gaussian  measure.   We  also  provide examples of measures having no t-neighborhood waist property, including a rather wide class\r\nof compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.\r\nWe  use  a  simpler  form  of  Gromov’s  pancake  argument  to  produce  some  estimates  of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures."}],"ec_funded":1,"date_updated":"2023-08-17T13:48:31Z","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.07350"}],"series_title":"LNM","publication":"Geometric Aspects of Functional Analysis","title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","external_id":{"arxiv":["1808.07350"],"isi":["000557689300003"]},"arxiv":1,"citation":{"ieee":"A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures,” in <i>Geometric Aspects of Functional Analysis</i>, vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” In <i>Geometric Aspects of Functional Analysis</i>, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">https://doi.org/10.1007/978-3-030-36020-7_1</a>.","ama":"Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Klartag B, Milman E, eds. <i>Geometric Aspects of Functional Analysis</i>. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:<a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">10.1007/978-3-030-36020-7_1</a>","mla":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” <i>Geometric Aspects of Functional Analysis</i>, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer Nature, 2020, pp. 1–27, doi:<a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">10.1007/978-3-030-36020-7_1</a>.","apa":"Akopyan, A., &#38; Karasev, R. (2020). Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In B. Klartag &#38; E. Milman (Eds.), <i>Geometric Aspects of Functional Analysis</i> (Vol. 2256, pp. 1–27). Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">https://doi.org/10.1007/978-3-030-36020-7_1</a>","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27.","ista":"Akopyan A, Karasev R. 2020.Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Geometric Aspects of Functional Analysis. vol. 2256, 1–27."},"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117"}],"scopus_import":"1","editor":[{"full_name":"Klartag, Bo'az","first_name":"Bo'az","last_name":"Klartag"},{"first_name":"Emanuel","full_name":"Milman, Emanuel","last_name":"Milman"}],"author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"}],"_id":"74","oa":1,"date_published":"2020-06-21T00:00:00Z","doi":"10.1007/978-3-030-36020-7_1","language":[{"iso":"eng"}],"year":"2020","publisher":"Springer Nature","type":"book_chapter","month":"06","publication_identifier":{"eissn":["16179692"],"issn":["00758434"],"isbn":["9783030360191"],"eisbn":["9783030360207"]},"quality_controlled":"1","isi":1,"volume":2256,"date_created":"2018-12-11T11:44:29Z","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","intvolume":"      2256"},{"type":"journal_article","doi":"10.1016/j.matpur.2020.02.008","language":[{"iso":"eng"}],"year":"2020","publisher":"Elsevier","date_published":"2020-07-01T00:00:00Z","author":[{"last_name":"Gladbach","full_name":"Gladbach, Peter","first_name":"Peter"},{"first_name":"Eva","full_name":"Kopfer, Eva","last_name":"Kopfer"},{"orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","first_name":"Jan","full_name":"Maas, Jan"},{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale","full_name":"Portinale, Lorenzo","first_name":"Lorenzo"}],"_id":"7573","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","intvolume":"       139","date_created":"2020-03-08T23:00:47Z","acknowledgement":"J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 716117). J.M. and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 350398276.","department":[{"_id":"JaMa"}],"isi":1,"article_type":"original","volume":139,"month":"07","publication_identifier":{"issn":["00217824"]},"quality_controlled":"1","status":"public","date_updated":"2023-09-07T13:31:05Z","day":"01","publication_status":"published","page":"204-234","oa_version":"Preprint","abstract":[{"lang":"eng","text":"This paper deals with dynamical optimal transport metrics defined by spatial discretisation of the Benamou–Benamou formula for the Kantorovich metric . Such metrics appear naturally in discretisations of -gradient flow formulations for dissipative PDE. However, it has recently been shown that these metrics do not in general converge to , unless strong geometric constraints are imposed on the discrete mesh. In this paper we prove that, in a 1-dimensional periodic setting, discrete transport metrics converge to a limiting transport metric with a non-trivial effective mobility. This mobility depends sensitively on the geometry of the mesh and on the non-local mobility at the discrete level. Our result quantifies to what extent discrete transport can make use of microstructure in the mesh to reduce the cost of transport."}],"ec_funded":1,"scopus_import":"1","issue":"7","citation":{"chicago":"Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of One-Dimensional Discrete Optimal Transport.” <i>Journal de Mathematiques Pures et Appliquees</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.matpur.2020.02.008\">https://doi.org/10.1016/j.matpur.2020.02.008</a>.","ieee":"P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of one-dimensional discrete optimal transport,” <i>Journal de Mathematiques Pures et Appliquees</i>, vol. 139, no. 7. Elsevier, pp. 204–234, 2020.","apa":"Gladbach, P., Kopfer, E., Maas, J., &#38; Portinale, L. (2020). Homogenisation of one-dimensional discrete optimal transport. <i>Journal de Mathematiques Pures et Appliquees</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.matpur.2020.02.008\">https://doi.org/10.1016/j.matpur.2020.02.008</a>","mla":"Gladbach, Peter, et al. “Homogenisation of One-Dimensional Discrete Optimal Transport.” <i>Journal de Mathematiques Pures et Appliquees</i>, vol. 139, no. 7, Elsevier, 2020, pp. 204–34, doi:<a href=\"https://doi.org/10.1016/j.matpur.2020.02.008\">10.1016/j.matpur.2020.02.008</a>.","ista":"Gladbach P, Kopfer E, Maas J, Portinale L. 2020. Homogenisation of one-dimensional discrete optimal transport. Journal de Mathematiques Pures et Appliquees. 139(7), 204–234.","short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Journal de Mathematiques Pures et Appliquees 139 (2020) 204–234.","ama":"Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of one-dimensional discrete optimal transport. <i>Journal de Mathematiques Pures et Appliquees</i>. 2020;139(7):204-234. doi:<a href=\"https://doi.org/10.1016/j.matpur.2020.02.008\">10.1016/j.matpur.2020.02.008</a>"},"arxiv":1,"project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020"},{"_id":"260482E2-B435-11E9-9278-68D0E5697425","name":"Taming Complexity in Partial Di erential Systems","grant_number":" F06504","call_identifier":"FWF"},{"name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","_id":"260788DE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"publication":"Journal de Mathematiques Pures et Appliquees","title":"Homogenisation of one-dimensional discrete optimal transport","external_id":{"arxiv":["1905.05757"],"isi":["000539439400008"]},"related_material":{"record":[{"status":"public","id":"10030","relation":"dissertation_contains"}]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1905.05757"}]},{"oa":1,"_id":"7629","author":[{"first_name":"Dominik L","full_name":"Forkert, Dominik L","id":"35C79D68-F248-11E8-B48F-1D18A9856A87","last_name":"Forkert"}],"date_published":"2020-03-31T00:00:00Z","publisher":"Institute of Science and Technology Austria","year":"2020","language":[{"iso":"eng"}],"doi":"10.15479/AT:ISTA:7629","type":"dissertation","publication_identifier":{"issn":["2663-337X"]},"month":"03","supervisor":[{"full_name":"Maas, Jan","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","orcid":"0000-0002-0845-1338"}],"department":[{"_id":"JaMa"}],"date_created":"2020-04-02T06:40:23Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["510"],"article_processing_charge":"No","file_date_updated":"2020-07-14T12:48:01Z","degree_awarded":"PhD","ec_funded":1,"abstract":[{"lang":"eng","text":"This thesis is based on three main topics: In the first part, we study convergence of discrete gradient flow structures associated with regular finite-volume discretisations of Fokker-Planck equations. We show evolutionary I convergence of the discrete gradient flows to the L2-Wasserstein gradient flow corresponding to the solution of a Fokker-Planck\r\nequation in arbitrary dimension d >= 1. Along the argument, we prove Mosco- and I-convergence results for discrete energy functionals, which are of independent interest for convergence of equivalent gradient flow structures in Hilbert spaces.\r\nThe second part investigates L2-Wasserstein flows on metric graph. The starting point is a Benamou-Brenier formula for the L2-Wasserstein distance, which is proved via a regularisation scheme for solutions of the continuity equation, adapted to the peculiar geometric structure of metric graphs. Based on those results, we show that the L2-Wasserstein space over a metric graph admits a gradient flow which may be identified as a solution of a Fokker-Planck equation.\r\nIn the third part, we focus again on the discrete gradient flows, already encountered in the first part. We propose a variational structure which extends the gradient flow structure to Markov chains violating the detailed-balance conditions. Using this structure, we characterise contraction estimates for the discrete heat flow in terms of convexity of\r\ncorresponding path-dependent energy functionals. In addition, we use this approach to derive several functional inequalities for said functionals."}],"oa_version":"Published Version","page":"154","publication_status":"published","day":"31","date_updated":"2023-09-07T13:03:12Z","status":"public","title":"Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains","file":[{"creator":"dernst","relation":"main_file","content_type":"application/pdf","access_level":"open_access","file_size":3297129,"file_name":"Thesis_Forkert_PDFA.pdf","date_updated":"2020-07-14T12:48:01Z","checksum":"c814a1a6195269ca6fe48b0dca45ae8a","date_created":"2020-04-14T10:47:59Z","file_id":"7657"},{"file_size":1063908,"file_name":"Thesis_Forkert_source.zip","date_updated":"2020-07-14T12:48:01Z","date_created":"2020-04-14T10:47:59Z","checksum":"ceafb53f923d1b5bdf14b2b0f22e4a81","file_id":"7658","creator":"dernst","relation":"source_file","content_type":"application/x-zip-compressed","access_level":"closed"}],"project":[{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"}],"citation":{"chicago":"Forkert, Dominik L. “Gradient Flows in Spaces of Probability Measures for Finite-Volume Schemes, Metric Graphs and Non-Reversible Markov Chains.” Institute of Science and Technology Austria, 2020. <a href=\"https://doi.org/10.15479/AT:ISTA:7629\">https://doi.org/10.15479/AT:ISTA:7629</a>.","ieee":"D. L. Forkert, “Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains,” Institute of Science and Technology Austria, 2020.","mla":"Forkert, Dominik L. <i>Gradient Flows in Spaces of Probability Measures for Finite-Volume Schemes, Metric Graphs and Non-Reversible Markov Chains</i>. Institute of Science and Technology Austria, 2020, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7629\">10.15479/AT:ISTA:7629</a>.","ista":"Forkert DL. 2020. Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains. Institute of Science and Technology Austria.","short":"D.L. Forkert, Gradient Flows in Spaces of Probability Measures for Finite-Volume Schemes, Metric Graphs and Non-Reversible Markov Chains, Institute of Science and Technology Austria, 2020.","apa":"Forkert, D. L. (2020). <i>Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:7629\">https://doi.org/10.15479/AT:ISTA:7629</a>","ama":"Forkert DL. Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains. 2020. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7629\">10.15479/AT:ISTA:7629</a>"},"alternative_title":["ISTA Thesis"],"has_accepted_license":"1"}]