[{"doi":"10.1007/s11118-023-10118-0","date_published":"2024-01-26T00:00:00Z","date_created":"2024-02-04T23:00:54Z","day":"26","publication":"Potential Analysis","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1572-929X"],"issn":["0926-2601"]},"publication_status":"epub_ahead","year":"2024","month":"01","publisher":"Springer Nature","quality_controlled":"1","scopus_import":"1","oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s11118-023-10118-0"}],"oa_version":"Published Version","acknowledgement":"The authors would like to thank Matthias Erbar and Ronan Herry for valuable discussions on this project. They are also grateful to Nathanaël Berestycki, and Fabrice Baudoin for respectively pointing out the references [7], and [6, 24], and to Julien Fageot and Thomas Letendre for pointing out a mistake in a previous version of the proof of Proposition 3.10. The authors feel very much indebted to an anonymous reviewer for his/her careful reading and the many valuable suggestions that have significantly contributed to the improvement of the paper. L.D.S. gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft through CRC 1060 as well as through SPP 2265, and by the Austrian Science Fund (FWF) grant F65 at Institute of Science and Technology Austria. This research was funded in whole or in part by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. E.K. and K.-T.S. gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft through the Hausdorff Center for Mathematics and through CRC 1060 as well as through SPP 2265.\r\nOpen Access funding enabled and organized by Projekt DEAL.","abstract":[{"lang":"eng","text":"We study random perturbations of a Riemannian manifold (M, g) by means of so-called\r\nFractional Gaussian Fields, which are defined intrinsically by the given manifold. The fields\r\nh• : ω \u0002→ hω will act on the manifold via the conformal transformation g \u0002→ gω := e2hω g.\r\nOur focus will be on the regular case with Hurst parameter H > 0, the critical case H = 0\r\nbeing the celebrated Liouville geometry in two dimensions. We want to understand how basic\r\ngeometric and functional-analytic quantities like diameter, volume, heat kernel, Brownian\r\nmotion, spectral bound, or spectral gap change under the influence of the noise. And if so, is\r\nit possible to quantify these dependencies in terms of key parameters of the noise? Another\r\ngoal is to define and analyze in detail the Fractional Gaussian Fields on a general Riemannian\r\nmanifold, a fascinating object of independent interest."}],"department":[{"_id":"JaMa"}],"title":"A discovery tour in random Riemannian geometry","author":[{"last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo"},{"full_name":"Kopfer, Eva","last_name":"Kopfer","first_name":"Eva"},{"last_name":"Sturm","full_name":"Sturm, Karl Theodor","first_name":"Karl Theodor"}],"article_processing_charge":"Yes (via OA deal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.” Potential Analysis, Springer Nature, 2024, doi:10.1007/s11118-023-10118-0.","ieee":"L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random Riemannian geometry,” Potential Analysis. Springer Nature, 2024.","short":"L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis (2024).","ama":"Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian geometry. Potential Analysis. 2024. doi:10.1007/s11118-023-10118-0","apa":"Dello Schiavo, L., Kopfer, E., & Sturm, K. T. (2024). A discovery tour in random Riemannian geometry. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-023-10118-0","chicago":"Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery Tour in Random Riemannian Geometry.” Potential Analysis. Springer Nature, 2024. https://doi.org/10.1007/s11118-023-10118-0.","ista":"Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian geometry. Potential Analysis."},"date_updated":"2024-02-05T13:04:23Z","status":"public","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"type":"journal_article","article_type":"original","_id":"14934"},{"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces."}],"intvolume":" 23","month":"01","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"creator":"dernst","date_updated":"2023-01-20T10:45:06Z","file_size":422612,"date_created":"2023-01-20T10:45:06Z","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"12325","checksum":"1f34f3e2cb521033de6154f274ea3a4e","success":1}],"publication_status":"published","publication_identifier":{"issn":["1424-3199"],"eissn":["1424-3202"]},"ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","issue":"1","volume":23,"_id":"12104","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)"},"type":"journal_article","article_type":"original","ddc":["510"],"date_updated":"2023-06-28T11:54:35Z","file_date_updated":"2023-01-20T10:45:06Z","department":[{"_id":"JaMa"}],"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).","oa":1,"quality_controlled":"1","publisher":"Springer Nature","publication":"Journal of Evolution Equations","day":"01","year":"2023","isi":1,"has_accepted_license":"1","date_created":"2023-01-08T23:00:53Z","date_published":"2023-01-01T00:00:00Z","doi":"10.1007/s00028-022-00859-7","article_number":"9","project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"},{"grant_number":"ESP156_N","name":"Gradient flow techniques for quantum Markov semigroups","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).","ieee":"L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms under order isomorphisms,” Journal of Evolution Equations, vol. 23, no. 1. Springer Nature, 2023.","ama":"Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 2023;23(1). doi:10.1007/s00028-022-00859-7","apa":"Dello Schiavo, L., & Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. Springer Nature. https://doi.org/10.1007/s00028-022-00859-7","mla":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations, vol. 23, no. 1, 9, Springer Nature, 2023, doi:10.1007/s00028-022-00859-7.","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","chicago":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations. Springer Nature, 2023. https://doi.org/10.1007/s00028-022-00859-7."},"title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000906214600004"]},"author":[{"last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo"},{"first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","last_name":"Wirth"}]},{"article_type":"original","type":"journal_article","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)"},"status":"public","_id":"12087","department":[{"_id":"JaMa"}],"file_date_updated":"2023-08-14T11:38:28Z","date_updated":"2023-08-14T11:39:28Z","ddc":["510"],"scopus_import":"1","month":"03","intvolume":" 24","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"}],"oa_version":"Published Version","volume":24,"ec_funded":1,"publication_identifier":{"issn":["1424-0637"]},"publication_status":"published","file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"14051","checksum":"8c7b185eba5ccd92ef55c120f654222c","creator":"dernst","file_size":554871,"date_updated":"2023-08-14T11:38:28Z","file_name":"2023_AnnalesHenriPoincare_Wirth.pdf","date_created":"2023-08-14T11:38:28Z"}],"language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"},{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"author":[{"last_name":"Wirth","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"},{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan","last_name":"Zhang","full_name":"Zhang, Haonan"}],"external_id":{"arxiv":["2105.08303"],"isi":["000837499800002"]},"article_processing_charge":"Yes (via OA deal)","title":"Curvature-dimension conditions for symmetric quantum Markov semigroups","citation":{"mla":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” Annales Henri Poincare, vol. 24, Springer Nature, 2023, pp. 717–50, doi:10.1007/s00023-022-01220-x.","short":"M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.","ieee":"M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum Markov semigroups,” Annales Henri Poincare, vol. 24. Springer Nature, pp. 717–750, 2023.","apa":"Wirth, M., & Zhang, H. (2023). Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-022-01220-x","ama":"Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 2023;24:717-750. doi:10.1007/s00023-022-01220-x","chicago":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” Annales Henri Poincare. Springer Nature, 2023. https://doi.org/10.1007/s00023-022-01220-x.","ista":"Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 24, 717–750."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publisher":"Springer Nature","oa":1,"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).","page":"717-750","doi":"10.1007/s00023-022-01220-x","date_published":"2023-03-01T00:00:00Z","date_created":"2022-09-11T22:01:57Z","isi":1,"has_accepted_license":"1","year":"2023","day":"01","publication":"Annales Henri Poincare"},{"date_created":"2021-10-17T22:01:17Z","doi":"10.1007/s11118-021-09951-y","date_published":"2023-03-01T00:00:00Z","page":"573-615","publication":"Potential Analysis","day":"01","year":"2023","has_accepted_license":"1","isi":1,"oa":1,"publisher":"Springer Nature","quality_controlled":"1","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.","title":"Ergodic decomposition of Dirichlet forms via direct integrals and applications","external_id":{"isi":["000704213400001"],"arxiv":["2003.01366"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals and applications,” Potential Analysis, vol. 58. Springer Nature, pp. 573–615, 2023.","short":"L. Dello Schiavo, Potential Analysis 58 (2023) 573–615.","apa":"Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 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Springer Nature, 2023. https://doi.org/10.1007/s11118-021-09951-y."},"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"ec_funded":1,"volume":58,"language":[{"iso":"eng"}],"file":[{"date_created":"2023-10-04T09:18:59Z","file_name":"2023_PotentialAnalysis_DelloSchiavo.pdf","date_updated":"2023-10-04T09:18:59Z","file_size":806391,"creator":"dernst","checksum":"625526482be300ca7281c91c30d41725","file_id":"14387","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"publication_status":"published","publication_identifier":{"eissn":["1572-929X"],"issn":["0926-2601"]},"intvolume":" 58","month":"03","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique.","lang":"eng"}],"department":[{"_id":"JaMa"}],"file_date_updated":"2023-10-04T09:18:59Z","ddc":["510"],"date_updated":"2023-10-04T09:19:12Z","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)"},"article_type":"original","type":"journal_article","_id":"10145"},{"date_updated":"2023-10-04T11:34:49Z","ddc":["510"],"file_date_updated":"2023-10-04T11:34:10Z","department":[{"_id":"JaMa"}],"_id":"12959","type":"journal_article","article_type":"original","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)"},"status":"public","publication_identifier":{"eissn":["1432-0835"],"issn":["0944-2669"]},"publication_status":"published","file":[{"date_created":"2023-10-04T11:34:10Z","file_name":"2023_CalculusEquations_Gladbach.pdf","creator":"dernst","date_updated":"2023-10-04T11:34:10Z","file_size":1240995,"file_id":"14393","checksum":"359bee38d94b7e0aa73925063cb8884d","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"issue":"5","volume":62,"ec_funded":1,"abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","scopus_import":"1","month":"04","intvolume":" 62","citation":{"chicago":"Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” Calculus of Variations and Partial Differential Equations. Springer Nature, 2023. https://doi.org/10.1007/s00526-023-02472-z.","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.” Calculus of Variations and Partial Differential Equations, vol. 62, no. 5, 143, Springer Nature, 2023, doi:10.1007/s00526-023-02472-z.","ieee":"P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of dynamical optimal transport on periodic graphs,” Calculus of Variations and Partial Differential Equations, vol. 62, no. 5. Springer Nature, 2023.","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., & Portinale, L. (2023). Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-023-02472-z","ama":"Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. 2023;62(5). doi:10.1007/s00526-023-02472-z"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Peter","last_name":"Gladbach","full_name":"Gladbach, Peter"},{"last_name":"Kopfer","full_name":"Kopfer, Eva","first_name":"Eva"},{"last_name":"Maas","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo","last_name":"Portinale","full_name":"Portinale, Lorenzo"}],"external_id":{"arxiv":["2110.15321"],"isi":["000980588900001"]},"article_processing_charge":"Yes (via OA deal)","title":"Homogenisation of dynamical optimal transport on periodic graphs","article_number":"143","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425"}],"has_accepted_license":"1","isi":1,"year":"2023","day":"28","publication":"Calculus of Variations and Partial Differential Equations","date_published":"2023-04-28T00:00:00Z","doi":"10.1007/s00526-023-02472-z","date_created":"2023-05-14T22:01:00Z","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).","quality_controlled":"1","publisher":"Springer Nature","oa":1},{"project":[{"grant_number":"716117","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","call_identifier":"H2020"},{"name":"Taming Complexity in Partial Di erential Systems","grant_number":" F06504","_id":"260482E2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"article_number":"109963","title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","author":[{"full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario"},{"full_name":"Gerolin, Augusto","last_name":"Gerolin","first_name":"Augusto"},{"full_name":"Portinale, Lorenzo","last_name":"Portinale","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000990804300001"],"arxiv":["2106.11217"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” Journal of Functional Analysis, vol. 285, no. 4. Elsevier, 2023.","short":"D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023).","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 2023;285(4). doi:10.1016/j.jfa.2023.109963","apa":"Feliciangeli, D., Gerolin, A., & Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.109963","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis, vol. 285, no. 4, 109963, Elsevier, 2023, doi:10.1016/j.jfa.2023.109963.","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.","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.109963."},"publisher":"Elsevier","quality_controlled":"1","oa":1,"acknowledgement":"This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813.","doi":"10.1016/j.jfa.2023.109963","date_published":"2023-08-15T00:00:00Z","date_created":"2023-05-07T22:01:02Z","day":"15","publication":"Journal of Functional Analysis","isi":1,"year":"2023","status":"public","article_type":"original","type":"journal_article","_id":"12911","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"date_updated":"2023-11-14T13:21:01Z","month":"08","intvolume":" 285","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem."}],"issue":"4","volume":285,"related_material":{"record":[{"id":"9792","status":"public","relation":"earlier_version"}]},"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"publication_status":"published"},{"type":"journal_article","article_type":"original","status":"public","_id":"13177","department":[{"_id":"JaMa"}],"date_updated":"2023-11-14T13:07:09Z","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1804.08353","open_access":"1"}],"scopus_import":"1","intvolume":" 151","month":"08","abstract":[{"text":"In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established.","lang":"eng"}],"oa_version":"Preprint","issue":"8","volume":151,"publication_status":"published","publication_identifier":{"eissn":["1088-6826"],"issn":["0002-9939"]},"language":[{"iso":"eng"}],"article_processing_charge":"No","external_id":{"arxiv":["1804.08353"],"isi":["000988204400001"]},"author":[{"first_name":"Bobo","full_name":"Hua, Bobo","last_name":"Hua"},{"first_name":"Matthias","last_name":"Keller","full_name":"Keller, Matthias"},{"full_name":"Schwarz, Michael","last_name":"Schwarz","first_name":"Michael"},{"last_name":"Wirth","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"title":"Sobolev-type inequalities and eigenvalue growth on graphs with finite measure","citation":{"ista":"Hua B, Keller M, Schwarz M, Wirth M. 2023. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. 151(8), 3401–3414.","chicago":"Hua, Bobo, Matthias Keller, Michael Schwarz, and Melchior Wirth. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” Proceedings of the American Mathematical Society. American Mathematical Society, 2023. https://doi.org/10.1090/proc/14361.","apa":"Hua, B., Keller, M., Schwarz, M., & Wirth, M. (2023). Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/14361","ama":"Hua B, Keller M, Schwarz M, Wirth M. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. 2023;151(8):3401-3414. doi:10.1090/proc/14361","short":"B. Hua, M. Keller, M. Schwarz, M. Wirth, Proceedings of the American Mathematical Society 151 (2023) 3401–3414.","ieee":"B. Hua, M. Keller, M. Schwarz, and M. Wirth, “Sobolev-type inequalities and eigenvalue growth on graphs with finite measure,” Proceedings of the American Mathematical Society, vol. 151, no. 8. American Mathematical Society, pp. 3401–3414, 2023.","mla":"Hua, Bobo, et al. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” Proceedings of the American Mathematical Society, vol. 151, no. 8, American Mathematical Society, 2023, pp. 3401–14, doi:10.1090/proc/14361."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"publisher":"American Mathematical Society","quality_controlled":"1","acknowledgement":"The second author was supported by the priority program SPP2026 of the German Research Foundation (DFG). The fourth author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2.","page":"3401-3414","date_created":"2023-07-02T22:00:43Z","date_published":"2023-08-01T00:00:00Z","doi":"10.1090/proc/14361","year":"2023","isi":1,"publication":"Proceedings of the American Mathematical Society","day":"01"},{"intvolume":" 28","month":"05","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes."}],"volume":28,"language":[{"iso":"eng"}],"file":[{"file_name":"2023_ElectronCommProbability_Schiavo.pdf","date_created":"2023-06-19T09:37:40Z","file_size":271434,"date_updated":"2023-06-19T09:37:40Z","creator":"dernst","success":1,"checksum":"4a543fe4b3f9e747cc52167c17bfb524","file_id":"13152","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"publication_status":"published","publication_identifier":{"eissn":["1083-589X"]},"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)"},"type":"journal_article","article_type":"original","_id":"13145","file_date_updated":"2023-06-19T09:37:40Z","department":[{"_id":"JaMa"}],"ddc":["510"],"date_updated":"2023-12-13T11:24:57Z","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","acknowledgement":"Research supported by the Sfb 1060 The Mathematics of Emergent Effects (University of Bonn). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through project ESPRIT 208.","date_created":"2023-06-18T22:00:48Z","doi":"10.1214/23-ECP528","date_published":"2023-05-05T00:00:00Z","page":"1-12","publication":"Electronic Communications in Probability","day":"05","year":"2023","has_accepted_license":"1","isi":1,"project":[{"grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"}],"title":"A Mecke-type characterization of the Dirichlet–Ferguson measure","article_processing_charge":"No","external_id":{"isi":["001042025400001"]},"author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo"},{"full_name":"Lytvynov, Eugene","last_name":"Lytvynov","first_name":"Eugene"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 28, 1–12.","chicago":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP528.","ama":"Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 2023;28:1-12. doi:10.1214/23-ECP528","apa":"Dello Schiavo, L., & Lytvynov, E. (2023). A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-ECP528","ieee":"L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson measure,” Electronic Communications in Probability, vol. 28. Institute of Mathematical Statistics, pp. 1–12, 2023.","short":"L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28 (2023) 1–12.","mla":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:10.1214/23-ECP528."}},{"date_created":"2023-07-30T22:01:03Z","doi":"10.1007/s00208-023-02680-0","date_published":"2023-07-24T00:00:00Z","publication":"Mathematische Annalen","day":"24","year":"2023","isi":1,"oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"The research of A.V. is supported by NSF DMS-1900286, DMS-2154402 and by Hausdorff Center for Mathematics. H.Z. is supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. This work is partially supported by NSF DMS-1929284 while both authors were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Harmonic Analysis and Convexity program.","title":"Noncommutative Bohnenblust–Hille inequalities","article_processing_charge":"No","external_id":{"arxiv":["2210.14468"],"isi":["001035665500001"]},"author":[{"last_name":"Volberg","full_name":"Volberg, Alexander","first_name":"Alexander"},{"full_name":"Zhang, Haonan","last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” Mathematische Annalen, Springer Nature, 2023, doi:10.1007/s00208-023-02680-0.","short":"A. Volberg, H. Zhang, Mathematische Annalen (2023).","ieee":"A. Volberg and H. Zhang, “Noncommutative Bohnenblust–Hille inequalities,” Mathematische Annalen. Springer Nature, 2023.","ama":"Volberg A, Zhang H. Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen. 2023. doi:10.1007/s00208-023-02680-0","apa":"Volberg, A., & Zhang, H. (2023). Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-023-02680-0","chicago":"Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” Mathematische Annalen. Springer Nature, 2023. https://doi.org/10.1007/s00208-023-02680-0.","ista":"Volberg A, Zhang H. 2023. Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen."},"project":[{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis"}],"language":[{"iso":"eng"}],"publication_status":"epub_ahead","publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"month":"07","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00208-023-02680-0"}],"scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow subexponentially in the degree (Defant et al. in Math Ann 374(1):653–680, 2019). Such inequalities have found great applications in learning low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions, 2022. arXiv preprint arXiv:2209.07279). The conjecture was resolved in Huang et al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894). In this paper, we give a new proof of these Bohnenblust–Hille inequalities for qubit system with constants that are dimension-free and of exponential growth in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials. Using similar ideas, we also study learning problems of low degree quantum observables and Bohr’s radius phenomenon on quantum Boolean cubes.","lang":"eng"}],"department":[{"_id":"JaMa"}],"date_updated":"2023-12-13T11:36:20Z","status":"public","type":"journal_article","article_type":"original","_id":"13318"},{"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Zhang H. 2023. Some convexity and monotonicity results of trace functionals. Annales Henri Poincare.","chicago":"Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.” Annales Henri Poincare. Springer Nature, 2023. https://doi.org/10.1007/s00023-023-01345-7.","short":"H. Zhang, Annales Henri Poincare (2023).","ieee":"H. Zhang, “Some convexity and monotonicity results of trace functionals,” Annales Henri Poincare. Springer Nature, 2023.","apa":"Zhang, H. (2023). Some convexity and monotonicity results of trace functionals. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-023-01345-7","ama":"Zhang H. Some convexity and monotonicity results of trace functionals. Annales Henri Poincare. 2023. doi:10.1007/s00023-023-01345-7","mla":"Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.” Annales Henri Poincare, Springer Nature, 2023, doi:10.1007/s00023-023-01345-7."},"title":"Some convexity and monotonicity results of trace functionals","external_id":{"arxiv":["2108.05785"],"isi":["001025709100001"]},"article_processing_charge":"No","author":[{"full_name":"Zhang, Haonan","last_name":"Zhang","first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"acknowledgement":"I am grateful to Boguslaw Zegarliński for asking me the questions in [3] and for helpful communication. I also want to thank Paata Ivanisvili for drawing [25] to my attention and for useful correspondence. Many thanks to the anonymous referee for the valuable comments and for pointing out some errors in an earlier version of the paper. This work is partially supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.","oa":1,"quality_controlled":"1","publisher":"Springer Nature","publication":"Annales Henri Poincare","day":"08","year":"2023","isi":1,"date_created":"2023-07-23T22:01:15Z","doi":"10.1007/s00023-023-01345-7","date_published":"2023-07-08T00:00:00Z","_id":"13271","status":"public","article_type":"original","type":"journal_article","date_updated":"2023-12-13T11:33:46Z","department":[{"_id":"JaMa"}],"oa_version":"Preprint","abstract":[{"text":"In this paper, we prove the convexity of trace functionals (A,B,C)↦Tr|BpACq|s,\r\nfor parameters (p, q, s) that are best possible, where B and C are any n-by-n positive-definite matrices, and A is any n-by-n matrix. We also obtain the monotonicity versions of trace functionals of this type. As applications, we extend some results in Carlen et al. (Linear Algebra Appl 490:174–185, 2016), Hiai and Petz (Publ Res Inst Math Sci 48(3):525-542, 2012) and resolve a conjecture in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) in the matrix setting. Other conjectures in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) will also be discussed. We also show that some related trace functionals are not concave in general. Such concavity results were expected to hold in different problems.","lang":"eng"}],"month":"07","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2108.05785","open_access":"1"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"epub_ahead","publication_identifier":{"issn":["1424-0637"]},"ec_funded":1},{"author":[{"last_name":"Olusanya","full_name":"Olusanya, Oluwafunmilola O","orcid":"0000-0003-1971-8314","id":"41AD96DC-F248-11E8-B48F-1D18A9856A87","first_name":"Oluwafunmilola O"},{"orcid":"0000-0002-6246-1465","full_name":"Khudiakova, Kseniia","last_name":"Khudiakova","first_name":"Kseniia","id":"4E6DC800-AE37-11E9-AC72-31CAE5697425"},{"id":"42377A0A-F248-11E8-B48F-1D18A9856A87","first_name":"Himani","full_name":"Sachdeva, Himani","last_name":"Sachdeva"}],"article_processing_charge":"No","department":[{"_id":"NiBa"},{"_id":"JaMa"}],"title":"Genetic load, eco-evolutionary feedback and extinction in a metapopulation","date_updated":"2024-01-26T12:00:53Z","citation":{"ieee":"O. O. Olusanya, K. Khudiakova, and H. Sachdeva, “Genetic load, eco-evolutionary feedback and extinction in a metapopulation,” bioRxiv. .","short":"O.O. Olusanya, K. Khudiakova, H. Sachdeva, BioRxiv (n.d.).","ama":"Olusanya OO, Khudiakova K, Sachdeva H. Genetic load, eco-evolutionary feedback and extinction in a metapopulation. bioRxiv. doi:10.1101/2023.12.02.569702","apa":"Olusanya, O. O., Khudiakova, K., & Sachdeva, H. (n.d.). Genetic load, eco-evolutionary feedback and extinction in a metapopulation. bioRxiv. https://doi.org/10.1101/2023.12.02.569702","mla":"Olusanya, Oluwafunmilola O., et al. “Genetic Load, Eco-Evolutionary Feedback and Extinction in a Metapopulation.” BioRxiv, doi:10.1101/2023.12.02.569702.","ista":"Olusanya OO, Khudiakova K, Sachdeva H. Genetic load, eco-evolutionary feedback and extinction in a metapopulation. bioRxiv, 10.1101/2023.12.02.569702.","chicago":"Olusanya, Oluwafunmilola O, Kseniia Khudiakova, and Himani Sachdeva. “Genetic Load, Eco-Evolutionary Feedback and Extinction in a Metapopulation.” BioRxiv, n.d. https://doi.org/10.1101/2023.12.02.569702."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","type":"preprint","tmp":{"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","image":"/images/cc_by_nc_nd.png"},"status":"public","project":[{"_id":"c08d3278-5a5b-11eb-8a69-fdb09b55f4b8","name":"Causes and consequences of population fragmentation","grant_number":"P32896"},{"_id":"34d33d68-11ca-11ed-8bc3-ec13763c0ca8","grant_number":"26293","name":"The impact of deleterious mutations on small populations"},{"_id":"34c872fe-11ca-11ed-8bc3-8534b82131e6","grant_number":"26380","name":"Polygenic Adaptation in a Metapopulation"}],"_id":"14732","doi":"10.1101/2023.12.02.569702","date_published":"2023-12-04T00:00:00Z","related_material":{"record":[{"status":"public","id":"14711","relation":"dissertation_contains"}]},"date_created":"2024-01-04T09:35:54Z","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","publication_status":"submitted","year":"2023","day":"04","publication":"bioRxiv","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://www.biorxiv.org/content/10.1101/2023.12.02.569702v1"}],"month":"12","abstract":[{"text":"Fragmented landscapes pose a significant threat to the persistence of species as they are highly susceptible to heightened risk of extinction due to the combined effects of genetic and demographic factors such as genetic drift and demographic stochasticity. This paper explores the intricate interplay between genetic load and extinction risk within metapopulations with a focus on understanding the impact of eco-evolutionary feedback mechanisms. We distinguish between two models of selection: soft selection, characterised by subpopulations maintaining carrying capacity despite load, and hard selection, where load can significantly affect population size. Within the soft selection framework, we investigate the impact of gene flow on genetic load at a single locus, while also considering the effect of selection strength and dominance coefficient. We subsequently build on this to examine how gene flow influences both population size and load under hard selection as well as identify critical thresholds for metapopulation persistence. Our analysis employs the diffusion, semi-deterministic and effective migration approximations. Our findings reveal that under soft selection, even modest levels of migration can significantly alleviate the burden of load. In sharp contrast, with hard selection, a much higher degree of gene flow is required to mitigate load and prevent the collapse of the metapopulation. Overall, this study sheds light into the crucial role migration plays in shaping the dynamics of genetic load and extinction risk in fragmented landscapes, offering valuable insights for conservation strategies and the preservation of diversity in a changing world.","lang":"eng"}],"oa_version":"Preprint"},{"oa":1,"quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"The authors are grateful to Martijn Caspers for helpful comments on a preliminary version of this manuscript. M. V. was supported by the NWO Vidi grant VI.Vidi.192.018 ‘Non-commutative harmonic analysis and rigidity of operator algebras’. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. Open access funding provided by Austrian Science Fund (FWF).","date_created":"2023-07-30T22:01:03Z","doi":"10.1007/s00220-023-04795-6","date_published":"2023-10-01T00:00:00Z","page":"381-416","publication":"Communications in Mathematical Physics","day":"01","year":"2023","isi":1,"has_accepted_license":"1","project":[{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N","name":"Gradient flow techniques for quantum Markov semigroups"}],"title":"Derivations and KMS-symmetric quantum Markov semigroups","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2303.15949"],"isi":["001033655400002"]},"author":[{"first_name":"Matthijs","full_name":"Vernooij, Matthijs","last_name":"Vernooij"},{"last_name":"Wirth","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","first_name":"Melchior"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Vernooij M, Wirth M. 2023. Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. 403, 381–416.","chicago":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” Communications in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04795-6.","ama":"Vernooij M, Wirth M. Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. 2023;403:381-416. doi:10.1007/s00220-023-04795-6","apa":"Vernooij, M., & Wirth, M. (2023). Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04795-6","short":"M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023) 381–416.","ieee":"M. Vernooij and M. Wirth, “Derivations and KMS-symmetric quantum Markov semigroups,” Communications in Mathematical Physics, vol. 403. Springer Nature, pp. 381–416, 2023.","mla":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” Communications in Mathematical Physics, vol. 403, Springer Nature, 2023, pp. 381–416, doi:10.1007/s00220-023-04795-6."},"intvolume":" 403","month":"10","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We prove that the generator of the L2 implementation of a KMS-symmetric quantum Markov semigroup can be expressed as the square of a derivation with values in a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups and the second-named author for GNS-symmetric semigroups. This result hinges on the introduction of a new completely positive map on the algebra of bounded operators on the GNS Hilbert space. This transformation maps symmetric Markov operators to symmetric Markov operators and is essential to obtain the required inner product on the Hilbert bimodule."}],"volume":403,"language":[{"iso":"eng"}],"file":[{"date_created":"2024-01-30T12:15:11Z","file_name":"2023_CommMathPhysics_Vernooij.pdf","creator":"dernst","date_updated":"2024-01-30T12:15:11Z","file_size":481209,"file_id":"14905","checksum":"cca204e81891270216a0c84eb8bcd398","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"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)"},"article_type":"original","type":"journal_article","_id":"13319","file_date_updated":"2024-01-30T12:15:11Z","department":[{"_id":"JaMa"}],"ddc":["510"],"date_updated":"2024-01-30T12:16:32Z"},{"article_processing_charge":"Yes (via OA deal)","author":[{"orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","first_name":"Melchior"}],"title":"Kac regularity and domination of quadratic forms","citation":{"chicago":"Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” Advances in Operator Theory. Springer Nature, 2022. https://doi.org/10.1007/s43036-022-00199-w.","ista":"Wirth M. 2022. Kac regularity and domination of quadratic forms. Advances in Operator Theory. 7(3), 38.","mla":"Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” Advances in Operator Theory, vol. 7, no. 3, 38, Springer Nature, 2022, doi:10.1007/s43036-022-00199-w.","short":"M. Wirth, Advances in Operator Theory 7 (2022).","ieee":"M. Wirth, “Kac regularity and domination of quadratic forms,” Advances in Operator Theory, vol. 7, no. 3. Springer Nature, 2022.","apa":"Wirth, M. (2022). Kac regularity and domination of quadratic forms. Advances in Operator Theory. Springer Nature. https://doi.org/10.1007/s43036-022-00199-w","ama":"Wirth M. Kac regularity and domination of quadratic forms. Advances in Operator Theory. 2022;7(3). doi:10.1007/s43036-022-00199-w"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"38","date_created":"2022-08-18T07:22:24Z","date_published":"2022-07-01T00:00:00Z","doi":"10.1007/s43036-022-00199-w","year":"2022","has_accepted_license":"1","publication":"Advances in Operator Theory","day":"01","oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"The author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2. The author would like to thank Daniel Lenz for his support and encouragement during the author’s ongoing graduate studies and him as well as Marcel Schmidt for fruitful discussions on domination of quadratic forms. He wants to thank Batu Güneysu and Peter Stollmann for valuable comments on a preliminary version of this article. He would also like to thank the organizers of the conference Analysis and Geometry on Graphs and Manifolds in Potsdam, where the initial motivation of this article was conceived, and the organizers of the intense activity period Metric Measure Spaces and Ricci Curvature at MPIM in Bonn, where this work was finished.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","department":[{"_id":"JaMa"}],"file_date_updated":"2022-08-18T08:02:34Z","date_updated":"2023-02-21T10:08:07Z","ddc":["510"],"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)"},"article_type":"original","type":"journal_article","keyword":["Algebra and Number Theory","Analysis"],"status":"public","_id":"11916","issue":"3","volume":7,"publication_status":"published","publication_identifier":{"eissn":["2538-225X"]},"language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"11921","checksum":"913474844a1b38264fb710746d5e2e98","creator":"dernst","file_size":389060,"date_updated":"2022-08-18T08:02:34Z","file_name":"2022_AdvancesOperatorTheory_Wirth.pdf","date_created":"2022-08-18T08:02:34Z"}],"scopus_import":"1","intvolume":" 7","month":"07","abstract":[{"lang":"eng","text":"A domain is called Kac regular for a quadratic form on L2 if every functions vanishing almost everywhere outside the domain can be approximated in form norm by functions with compact support in the domain. It is shown that this notion is stable under domination of quadratic forms. As applications measure perturbations of quasi-regular Dirichlet forms, Cheeger energies on metric measure spaces and Schrödinger operators on manifolds are studied. Along the way a characterization of the Sobolev space with Dirichlet boundary conditions on domains in infinitesimally Riemannian metric measure spaces is obtained."}],"oa_version":"Published Version"},{"scopus_import":"1","intvolume":" 9","month":"11","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."}],"oa_version":"Published Version","ec_funded":1,"issue":"43","volume":9,"publication_status":"published","publication_identifier":{"issn":["2330-1511"]},"language":[{"iso":"eng"}],"file":[{"date_created":"2023-01-26T13:02:07Z","file_name":"2022_ProceedingsAMS_Cremaschi.pdf","creator":"dernst","date_updated":"2023-01-26T13:02:07Z","file_size":326471,"file_id":"12404","checksum":"cb4a79937c1f60d4c329a10ee797f0d2","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"tmp":{"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","image":"/images/cc_by_nc_nd.png"},"type":"journal_article","article_type":"original","status":"public","_id":"12177","file_date_updated":"2023-01-26T13:02:07Z","department":[{"_id":"JaMa"}],"date_updated":"2023-01-26T13:04:13Z","ddc":["510"],"oa":1,"publisher":"American Mathematical Society","quality_controlled":"1","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.","page":"445-459","date_created":"2023-01-12T12:12:17Z","date_published":"2022-11-02T00:00:00Z","doi":"10.1090/bproc/134","year":"2022","has_accepted_license":"1","publication":"Proceedings of the American Mathematical Society, Series B","day":"02","project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"article_processing_charge":"No","author":[{"first_name":"Tommaso","last_name":"Cremaschi","full_name":"Cremaschi, Tommaso"},{"last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"}],"title":"Effective contraction of Skinning maps","citation":{"ista":"Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 9(43), 445–459.","chicago":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” Proceedings of the American Mathematical Society, Series B. American Mathematical Society, 2022. https://doi.org/10.1090/bproc/134.","apa":"Cremaschi, T., & Dello Schiavo, L. (2022). Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. American Mathematical Society. https://doi.org/10.1090/bproc/134","ama":"Cremaschi T, Dello Schiavo L. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 2022;9(43):445-459. doi:10.1090/bproc/134","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,” Proceedings of the American Mathematical Society, Series B, vol. 9, no. 43. American Mathematical Society, pp. 445–459, 2022.","mla":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” Proceedings of the American Mathematical Society, Series B, vol. 9, no. 43, American Mathematical Society, 2022, pp. 445–59, doi:10.1090/bproc/134."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"keyword":["quasi curvature-dimension condition","sub-riemannian geometry","Sobolev-to-Lipschitz property","Varadhan short-time asymptotics"],"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)"},"type":"journal_article","article_type":"original","_id":"10588","file_date_updated":"2022-01-03T11:08:31Z","department":[{"_id":"JaMa"}],"ddc":["510"],"date_updated":"2023-08-02T13:39:05Z","intvolume":" 384","month":"12","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds.","lang":"eng"}],"ec_funded":1,"volume":384,"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"2593abbf195e38efa93b6006b1e90eb1","file_id":"10596","file_size":410090,"date_updated":"2022-01-03T11:08:31Z","creator":"alisjak","file_name":"2021_MathAnn_DelloSchiavo.pdf","date_created":"2022-01-03T11:08:31Z"}],"publication_status":"published","publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"title":"Sobolev-to-Lipschitz property on QCD- spaces and applications","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2110.05137"],"isi":["000734150200001"]},"author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo"},{"first_name":"Kohei","full_name":"Suzuki, Kohei","last_name":"Suzuki"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” Mathematische Annalen. Springer Nature, 2022. https://doi.org/10.1007/s00208-021-02331-2.","ista":"Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 384, 1815–1832.","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” Mathematische Annalen, vol. 384, Springer Nature, 2022, pp. 1815–32, doi:10.1007/s00208-021-02331-2.","ama":"Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 2022;384:1815-1832. doi:10.1007/s00208-021-02331-2","apa":"Dello Schiavo, L., & Suzuki, K. (2022). Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-021-02331-2","ieee":"L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces and applications,” Mathematische Annalen, vol. 384. Springer Nature, pp. 1815–1832, 2022.","short":"L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832."},"oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"The authors are grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino Antonelli for reading a preliminary version of this work and for their valuable comments and suggestions. Finally, they wish to express their gratitude to two anonymous Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S. gratefully acknowledges funding of his position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium.","date_created":"2022-01-02T23:01:35Z","doi":"10.1007/s00208-021-02331-2","date_published":"2022-12-01T00:00:00Z","page":"1815-1832","publication":"Mathematische Annalen","day":"01","year":"2022","isi":1,"has_accepted_license":"1"},{"ddc":["510","530"],"date_updated":"2023-08-03T06:37:49Z","department":[{"_id":"JaMa"}],"file_date_updated":"2022-04-29T11:24:23Z","_id":"11330","status":"public","article_type":"original","type":"journal_article","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)"},"file":[{"creator":"dernst","date_updated":"2022-04-29T11:24:23Z","file_size":362119,"date_created":"2022-04-29T11:24:23Z","file_name":"2022_JourStatisticalPhysics_Wirth.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"f3e0b00884b7dde31347a3756788b473","file_id":"11338","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"publication_status":"published","volume":187,"issue":"2","ec_funded":1,"oa_version":"Published Version","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."}],"month":"04","intvolume":" 187","scopus_import":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” Journal of Statistical Physics, vol. 187, no. 2, 19, Springer Nature, 2022, doi:10.1007/s10955-022-02911-9.","apa":"Wirth, M. (2022). A dual formula for the noncommutative transport distance. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02911-9","ama":"Wirth M. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 2022;187(2). doi:10.1007/s10955-022-02911-9","ieee":"M. Wirth, “A dual formula for the noncommutative transport distance,” Journal of Statistical Physics, vol. 187, no. 2. Springer Nature, 2022.","short":"M. Wirth, Journal of Statistical Physics 187 (2022).","chicago":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02911-9.","ista":"Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19."},"title":"A dual formula for the noncommutative transport distance","author":[{"last_name":"Wirth","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000780305000001"]},"article_number":"19","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"day":"08","publication":"Journal of Statistical Physics","isi":1,"has_accepted_license":"1","year":"2022","doi":"10.1007/s10955-022-02911-9","date_published":"2022-04-08T00:00:00Z","date_created":"2022-04-24T22:01:43Z","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).","quality_controlled":"1","publisher":"Springer Nature","oa":1},{"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"05a1fe7d10914a00c2bca9b447993a65","file_id":"11455","success":1,"date_updated":"2022-06-20T07:51:32Z","file_size":463025,"creator":"dernst","date_created":"2022-06-20T07:51:32Z","file_name":"2022_BulletinMathBiology_Saona.pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0092-8240"],"eissn":["1522-9602"]},"publication_status":"published","issue":"8","related_material":{"link":[{"url":"https://doi.org/10.1007/s11538-022-01118-z","relation":"erratum"}]},"volume":84,"ec_funded":1,"oa_version":"Published Version","abstract":[{"text":"Empirical essays of fitness landscapes suggest that they may be rugged, that is having multiple fitness peaks. Such fitness landscapes, those that have multiple peaks, necessarily have special local structures, called reciprocal sign epistasis (Poelwijk et al. in J Theor Biol 272:141–144, 2011). Here, we investigate the quantitative relationship between the number of fitness peaks and the number of reciprocal sign epistatic interactions. Previously, it has been shown (Poelwijk et al. in J Theor Biol 272:141–144, 2011) that pairwise reciprocal sign epistasis is a necessary but not sufficient condition for the existence of multiple peaks. Applying discrete Morse theory, which to our knowledge has never been used in this context, we extend this result by giving the minimal number of reciprocal sign epistatic interactions required to create a given number of peaks.","lang":"eng"}],"month":"06","intvolume":" 84","scopus_import":"1","ddc":["510","570"],"date_updated":"2023-08-03T07:20:53Z","department":[{"_id":"GradSch"},{"_id":"NiBa"},{"_id":"JaMa"}],"file_date_updated":"2022-06-20T07:51:32Z","_id":"11447","status":"public","keyword":["Computational Theory and Mathematics","General Agricultural and Biological Sciences","Pharmacology","General Environmental Science","General Biochemistry","Genetics and Molecular Biology","General Mathematics","Immunology","General Neuroscience"],"type":"journal_article","article_type":"original","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":"17","publication":"Bulletin of Mathematical Biology","isi":1,"has_accepted_license":"1","year":"2022","doi":"10.1007/s11538-022-01029-z","date_published":"2022-06-17T00:00:00Z","date_created":"2022-06-17T16:16:15Z","acknowledgement":"We are grateful to Herbert Edelsbrunner and Jeferson Zapata for helpful discussions. Open access funding provided by Austrian Science Fund (FWF). Partially supported by the ERC Consolidator (771209–CharFL) and the FWF Austrian Science Fund (I5127-B) grants to FAK.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ieee":"R. J. Saona Urmeneta, F. Kondrashov, and K. Khudiakova, “Relation between the number of peaks and the number of reciprocal sign epistatic interactions,” Bulletin of Mathematical Biology, vol. 84, no. 8. Springer Nature, 2022.","short":"R.J. Saona Urmeneta, F. Kondrashov, K. Khudiakova, Bulletin of Mathematical Biology 84 (2022).","ama":"Saona Urmeneta RJ, Kondrashov F, Khudiakova K. Relation between the number of peaks and the number of reciprocal sign epistatic interactions. Bulletin of Mathematical Biology. 2022;84(8). doi:10.1007/s11538-022-01029-z","apa":"Saona Urmeneta, R. J., Kondrashov, F., & Khudiakova, K. (2022). Relation between the number of peaks and the number of reciprocal sign epistatic interactions. Bulletin of Mathematical Biology. Springer Nature. https://doi.org/10.1007/s11538-022-01029-z","mla":"Saona Urmeneta, Raimundo J., et al. “Relation between the Number of Peaks and the Number of Reciprocal Sign Epistatic Interactions.” Bulletin of Mathematical Biology, vol. 84, no. 8, 74, Springer Nature, 2022, doi:10.1007/s11538-022-01029-z.","ista":"Saona Urmeneta RJ, Kondrashov F, Khudiakova K. 2022. Relation between the number of peaks and the number of reciprocal sign epistatic interactions. Bulletin of Mathematical Biology. 84(8), 74.","chicago":"Saona Urmeneta, Raimundo J, Fyodor Kondrashov, and Kseniia Khudiakova. “Relation between the Number of Peaks and the Number of Reciprocal Sign Epistatic Interactions.” Bulletin of Mathematical Biology. Springer Nature, 2022. https://doi.org/10.1007/s11538-022-01029-z."},"title":"Relation between the number of peaks and the number of reciprocal sign epistatic interactions","author":[{"last_name":"Saona Urmeneta","full_name":"Saona Urmeneta, Raimundo J","orcid":"0000-0001-5103-038X","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425","first_name":"Raimundo J"},{"first_name":"Fyodor","id":"44FDEF62-F248-11E8-B48F-1D18A9856A87","last_name":"Kondrashov","orcid":"0000-0001-8243-4694","full_name":"Kondrashov, Fyodor"},{"first_name":"Kseniia","id":"4E6DC800-AE37-11E9-AC72-31CAE5697425","last_name":"Khudiakova","orcid":"0000-0002-6246-1465","full_name":"Khudiakova, Kseniia"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000812509800001"]},"article_number":"74","project":[{"grant_number":"771209","name":"Characterizing the fitness landscape on population and global scales","_id":"26580278-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Evolutionary analysis of gene regulation","grant_number":"I05127","_id":"c098eddd-5a5b-11eb-8a69-abe27170a68f"}]},{"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.","quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics","oa":1,"day":"18","publication":"SIAM Journal on Mathematical Analysis","isi":1,"year":"2022","doi":"10.1137/21M1410968","date_published":"2022-07-18T00:00:00Z","date_created":"2022-08-07T22:01:59Z","page":"4297-4333","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","chicago":"Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21M1410968.","apa":"Forkert, D. L., Maas, J., & Portinale, L. (2022). Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21M1410968","ama":"Forkert DL, Maas J, Portinale L. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. 2022;54(4):4297-4333. doi:10.1137/21M1410968","ieee":"D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” SIAM Journal on Mathematical Analysis, vol. 54, no. 4. Society for Industrial and Applied Mathematics, pp. 4297–4333, 2022.","short":"D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis 54 (2022) 4297–4333.","mla":"Forkert, Dominik L., et al. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” SIAM Journal on Mathematical Analysis, vol. 54, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 4297–333, doi:10.1137/21M1410968."},"title":"Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions","author":[{"id":"35C79D68-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik L","last_name":"Forkert","full_name":"Forkert, Dominik L"},{"first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas"},{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo","last_name":"Portinale","full_name":"Portinale, Lorenzo"}],"article_processing_charge":"No","external_id":{"arxiv":["2008.10962"],"isi":["000889274600001"]},"oa_version":"Preprint","abstract":[{"lang":"eng","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."}],"month":"07","intvolume":" 54","scopus_import":"1","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2008.10962"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"publication_status":"published","related_material":{"record":[{"relation":"earlier_version","id":"10022","status":"public"}]},"volume":54,"issue":"4","ec_funded":1,"_id":"11739","status":"public","keyword":["Fokker--Planck equation","gradient flow","evolutionary $\\Gamma$-convergence"],"type":"journal_article","article_type":"original","date_updated":"2023-08-03T12:37:21Z","department":[{"_id":"JaMa"}]},{"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.05677"}],"month":"10","intvolume":" 17","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."}],"oa_version":"Preprint","issue":"5","volume":17,"ec_funded":1,"publication_identifier":{"eissn":["1556-181X"],"issn":["1556-1801"]},"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","article_type":"original","status":"public","_id":"11700","department":[{"_id":"JaMa"}],"date_updated":"2023-08-03T12:25:49Z","publisher":"American Institute of Mathematical Sciences","quality_controlled":"1","oa":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.","page":"687-717","date_published":"2022-10-01T00:00:00Z","doi":"10.3934/nhm.2022023","date_created":"2022-07-31T22:01:46Z","isi":1,"year":"2022","day":"01","publication":"Networks and Heterogeneous Media","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"author":[{"first_name":"Matthias","last_name":"Erbar","full_name":"Erbar, Matthias"},{"full_name":"Forkert, Dominik L","last_name":"Forkert","id":"35C79D68-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik L"},{"full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"},{"last_name":"Mugnolo","full_name":"Mugnolo, Delio","first_name":"Delio"}],"article_processing_charge":"No","external_id":{"isi":["000812422100001"],"arxiv":["2105.05677"]},"title":"Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph","citation":{"chicago":"Erbar, Matthias, Dominik L Forkert, Jan Maas, and Delio Mugnolo. “Gradient Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric Graph.” Networks and Heterogeneous Media. American Institute of Mathematical Sciences, 2022. https://doi.org/10.3934/nhm.2022023.","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.” Networks and Heterogeneous Media, vol. 17, no. 5, American Institute of Mathematical Sciences, 2022, pp. 687–717, doi:10.3934/nhm.2022023.","short":"M. Erbar, D.L. Forkert, J. Maas, D. Mugnolo, Networks and Heterogeneous Media 17 (2022) 687–717.","ieee":"M. Erbar, D. L. Forkert, J. Maas, and D. Mugnolo, “Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph,” Networks and Heterogeneous Media, vol. 17, no. 5. American Institute of Mathematical Sciences, pp. 687–717, 2022.","ama":"Erbar M, Forkert DL, Maas J, Mugnolo D. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media. 2022;17(5):687-717. doi:10.3934/nhm.2022023","apa":"Erbar, M., Forkert, D. L., Maas, J., & Mugnolo, D. (2022). Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media. American Institute of Mathematical Sciences. https://doi.org/10.3934/nhm.2022023"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"isi":1,"year":"2022","day":"01","publication":"Mathematische Zeitschrift","page":"2327-2352","date_published":"2022-12-01T00:00:00Z","doi":"10.1007/s00209-022-03143-z","date_created":"2023-01-16T09:45:31Z","acknowledgement":"Yu. K. thanks Professor Waldemar Hebisch for valuable discussions on the general context of multipliers on Lie groups. This work was started during an ICL-CNRS fellowship of the second\r\nnamed author at the Imperial College London. Yu. K. is supported by the ANR-19-CE40-0002 grant of the French National Research Agency (ANR). 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. R. A. was supported by the EPSRC grant EP/R003025. M. R. is supported by the EPSRC grant EP/R003025/2 and by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"citation":{"short":"R. Akylzhanov, Y. Kuznetsova, M. Ruzhansky, H. Zhang, Mathematische Zeitschrift 302 (2022) 2327–2352.","ieee":"R. Akylzhanov, Y. Kuznetsova, M. Ruzhansky, and H. Zhang, “Norms of certain functions of a distinguished Laplacian on the ax + b groups,” Mathematische Zeitschrift, vol. 302, no. 4. Springer Nature, pp. 2327–2352, 2022.","apa":"Akylzhanov, R., Kuznetsova, Y., Ruzhansky, M., & Zhang, H. (2022). Norms of certain functions of a distinguished Laplacian on the ax + b groups. Mathematische Zeitschrift. Springer Nature. https://doi.org/10.1007/s00209-022-03143-z","ama":"Akylzhanov R, Kuznetsova Y, Ruzhansky M, Zhang H. Norms of certain functions of a distinguished Laplacian on the ax + b groups. Mathematische Zeitschrift. 2022;302(4):2327-2352. doi:10.1007/s00209-022-03143-z","mla":"Akylzhanov, Rauan, et al. “Norms of Certain Functions of a Distinguished Laplacian on the Ax + b Groups.” Mathematische Zeitschrift, vol. 302, no. 4, Springer Nature, 2022, pp. 2327–52, doi:10.1007/s00209-022-03143-z.","ista":"Akylzhanov R, Kuznetsova Y, Ruzhansky M, Zhang H. 2022. Norms of certain functions of a distinguished Laplacian on the ax + b groups. Mathematische Zeitschrift. 302(4), 2327–2352.","chicago":"Akylzhanov, Rauan, Yulia Kuznetsova, Michael Ruzhansky, and Haonan Zhang. “Norms of Certain Functions of a Distinguished Laplacian on the Ax + b Groups.” Mathematische Zeitschrift. Springer Nature, 2022. https://doi.org/10.1007/s00209-022-03143-z."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Rauan","last_name":"Akylzhanov","full_name":"Akylzhanov, Rauan"},{"last_name":"Kuznetsova","full_name":"Kuznetsova, Yulia","first_name":"Yulia"},{"last_name":"Ruzhansky","full_name":"Ruzhansky, Michael","first_name":"Michael"},{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan","last_name":"Zhang","full_name":"Zhang, Haonan"}],"article_processing_charge":"No","external_id":{"isi":["000859680700001"],"arxiv":["2101.00584"]},"title":"Norms of certain functions of a distinguished Laplacian on the ax + b groups","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"}],"publication_identifier":{"eissn":["1432-1823"],"issn":["0025-5874"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"4","volume":302,"ec_funded":1,"abstract":[{"text":"The aim of this paper is to find new estimates for the norms of functions of a (minus) distinguished Laplace operator L on the ‘ax+b’ groups. The central part is devoted to spectrally localized wave propagators, that is, functions of the type ψ(L−−√)exp(itL−−√), with ψ∈C0(R). We show that for t→+∞, the convolution kernel kt of this operator satisfies\r\n∥kt∥1≍t,∥kt∥∞≍1,\r\nso that the upper estimates of D. Müller and C. Thiele (Studia Math., 2007) are sharp. As a necessary component, we recall the Plancherel density of L and spend certain time presenting and comparing different approaches to its calculation. Using its explicit form, we estimate uniform norms of several functions of the shifted Laplace-Beltrami operator Δ~, closely related to L. The functions include in particular exp(−tΔ~γ), t>0,γ>0, and (Δ~−z)s, with complex z, s.","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/2101.00584","open_access":"1"}],"month":"12","intvolume":" 302","date_updated":"2023-08-04T09:22:14Z","department":[{"_id":"JaMa"}],"_id":"12210","article_type":"original","type":"journal_article","status":"public","keyword":["General Mathematics"]},{"page":"289-310","date_published":"2022-12-01T00:00:00Z","doi":"10.1016/j.laa.2022.09.001","date_created":"2023-01-16T09:46:38Z","isi":1,"has_accepted_license":"1","year":"2022","day":"01","publication":"Linear Algebra and its Applications","quality_controlled":"1","publisher":"Elsevier","oa":1,"acknowledgement":"Work partially supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.","author":[{"first_name":"Eric A.","full_name":"Carlen, Eric A.","last_name":"Carlen"},{"full_name":"Zhang, Haonan","last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000860689600014"]},"title":"Monotonicity versions of Epstein's concavity theorem and related inequalities","citation":{"short":"E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.","ieee":"E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem and related inequalities,” Linear Algebra and its Applications, vol. 654. Elsevier, pp. 289–310, 2022.","ama":"Carlen EA, Zhang H. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 2022;654:289-310. doi:10.1016/j.laa.2022.09.001","apa":"Carlen, E. A., & Zhang, H. (2022). Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2022.09.001","mla":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” Linear Algebra and Its Applications, vol. 654, Elsevier, 2022, pp. 289–310, doi:10.1016/j.laa.2022.09.001.","ista":"Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 654, 289–310.","chicago":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” Linear Algebra and Its Applications. Elsevier, 2022. https://doi.org/10.1016/j.laa.2022.09.001."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis"}],"volume":654,"publication_identifier":{"issn":["0024-3795"]},"publication_status":"published","file":[{"date_updated":"2023-01-27T08:08:39Z","file_size":441184,"creator":"dernst","date_created":"2023-01-27T08:08:39Z","file_name":"2022_LinearAlgebra_Carlen.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"12415","checksum":"cf3cb7e7e34baa967849f01d8f0c1ae4","success":1}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"12","intvolume":" 654","abstract":[{"lang":"eng","text":"Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments."}],"oa_version":"Published Version","file_date_updated":"2023-01-27T08:08:39Z","department":[{"_id":"JaMa"}],"date_updated":"2023-08-04T09:24:51Z","ddc":["510"],"article_type":"original","type":"journal_article","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)"},"status":"public","keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Numerical Analysis","Algebra and Number Theory"],"_id":"12216"},{"acknowledgement":"C.F. and P.G. thank FCT/Portugal for support through the project UID/MAT/04459/2013.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative programme (grant agreement No. 715734). F.S. was founded by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.\r\nF.S. wishes to thank Joe P. Chen for some fruitful discussions at an early stage of this work. F.S. thanks CAMGSD, IST, Lisbon, where part of this work has been done, and the European research and innovative programme No. 715734 for the kind hospitality.","publisher":"Bernoulli Society for Mathematical Statistics and Probability","quality_controlled":"1","oa":1,"day":"01","publication":"Bernoulli","isi":1,"year":"2022","date_published":"2022-05-01T00:00:00Z","doi":"10.3150/21-bej1390","date_created":"2023-01-16T10:03:04Z","page":"1340-1381","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Franceschini C, Gonçalves P, Sau F. 2022. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 28(2), 1340–1381.","chicago":"Franceschini, Chiara, Patrícia Gonçalves, and Federico Sau. “Symmetric Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” Bernoulli. Bernoulli Society for Mathematical Statistics and Probability, 2022. https://doi.org/10.3150/21-bej1390.","short":"C. Franceschini, P. Gonçalves, F. Sau, Bernoulli 28 (2022) 1340–1381.","ieee":"C. Franceschini, P. Gonçalves, and F. Sau, “Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics,” Bernoulli, vol. 28, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1340–1381, 2022.","ama":"Franceschini C, Gonçalves P, Sau F. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 2022;28(2):1340-1381. doi:10.3150/21-bej1390","apa":"Franceschini, C., Gonçalves, P., & Sau, F. (2022). Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. Bernoulli Society for Mathematical Statistics and Probability. https://doi.org/10.3150/21-bej1390","mla":"Franceschini, Chiara, et al. “Symmetric Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” Bernoulli, vol. 28, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2022, pp. 1340–81, doi:10.3150/21-bej1390."},"title":"Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics","author":[{"full_name":"Franceschini, Chiara","last_name":"Franceschini","first_name":"Chiara"},{"first_name":"Patrícia","last_name":"Gonçalves","full_name":"Gonçalves, Patrícia"},{"last_name":"Sau","full_name":"Sau, Federico","first_name":"Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425"}],"external_id":{"isi":["000766619100025"],"arxiv":["2007.11998"]},"article_processing_charge":"No","oa_version":"Preprint","abstract":[{"text":"We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary conditions as hydrodynamic equation. In our approach, we combine duality and first-second class particle techniques to reduce the scaling limit of the inclusion process to the limiting behavior of a single, non-interacting, particle.","lang":"eng"}],"month":"05","intvolume":" 28","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2007.11998"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1350-7265"]},"publication_status":"published","volume":28,"issue":"2","ec_funded":1,"_id":"12281","status":"public","keyword":["Statistics and Probability"],"type":"journal_article","article_type":"original","date_updated":"2023-08-04T10:27:35Z","department":[{"_id":"JaMa"}]},{"article_type":"original","type":"journal_article","status":"public","_id":"10797","department":[{"_id":"JaMa"}],"date_updated":"2023-10-17T12:49:43Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2007.08272"}],"scopus_import":"1","intvolume":" 58","month":"02","abstract":[{"text":"We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then we derive new orthogonal polynomial dualities. From the classical dualities, we derive the uniqueness of the non-equilibrium steady state and obtain correlation inequalities. Starting from the orthogonal polynomial dualities, we show universal properties of n-point correlation functions in the non-equilibrium steady state for systems with at most two different reservoir parameters, such as a chain with reservoirs at left and right ends.","lang":"eng"},{"lang":"fre","text":"Nous considérons des processus d’exclusion partielle, et des processus d’inclusion sur un graphe général en contact avec des réservoirs. Nous autorisons la présence de inhomogenéités sur les arrêts ainsi que sur les sommets du graph. Nous généralisons les “dualités classiques” dans ce contexte et nous démontrons des nouvelles dualités orthogonales. À partir des dualités classiques, nous démontrons l’unicité de l’état stationnaire non-équilibre, ainsi que des inégalités de corrélation. À partir des dualités orthogonales nous démontrons des propriétés universelles des fonctions de corrélation à n points dans l’état stationnaire non-équilibre pour des systèmes avec deux paramètres de réservoirs inégaux, comme par exemple une chaîne avec des réservoirs à droite et à gauche."}],"oa_version":"Preprint","ec_funded":1,"volume":58,"issue":"1","publication_status":"published","publication_identifier":{"issn":["0246-0203"]},"language":[{"iso":"eng"}],"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"article_processing_charge":"No","external_id":{"arxiv":["2007.08272"],"isi":["000752489300010"]},"author":[{"first_name":"Simone","last_name":"Floreani","full_name":"Floreani, Simone"},{"first_name":"Frank","full_name":"Redig, Frank","last_name":"Redig"},{"last_name":"Sau","full_name":"Sau, Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico"}],"title":"Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations","citation":{"apa":"Floreani, S., Redig, F., & Sau, F. (2022). Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AIHP1163","ama":"Floreani S, Redig F, Sau F. Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2022;58(1):220-247. doi:10.1214/21-AIHP1163","ieee":"S. Floreani, F. Redig, and F. Sau, “Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 58, no. 1. Institute of Mathematical Statistics, pp. 220–247, 2022.","short":"S. Floreani, F. Redig, F. Sau, Annales de l’institut Henri Poincare (B) Probability and Statistics 58 (2022) 220–247.","mla":"Floreani, Simone, et al. “Orthogonal Polynomial Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 58, no. 1, Institute of Mathematical Statistics, 2022, pp. 220–47, doi:10.1214/21-AIHP1163.","ista":"Floreani S, Redig F, Sau F. 2022. Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. Annales de l’institut Henri Poincare (B) Probability and Statistics. 58(1), 220–247.","chicago":"Floreani, Simone, Frank Redig, and Federico Sau. “Orthogonal Polynomial Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AIHP1163."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","acknowledgement":"The authors would like to thank Gioia Carinci and Cristian Giardinà for useful discussions. F.R. and S.F. thank Jean-René Chazottes for a stay at CPHT (Institut Polytechnique de Paris), in the realm of Chaire d’Alembert (Paris-Saclay University), where part of this work was performed. S.F. acknowledges Simona Villa for her support in creating the picture. S.F. acknowledges financial support from NWO via the grant TOP1.17.019. F.S. acknowledges financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.","page":"220-247","date_created":"2022-02-27T23:01:50Z","date_published":"2022-02-01T00:00:00Z","doi":"10.1214/21-AIHP1163","year":"2022","isi":1,"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","day":"01"},{"project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1541.","ista":"Dello Schiavo L. 2022. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. 50(2), 591–648.","mla":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability, vol. 50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:10.1214/21-AOP1541.","short":"L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.","ieee":"L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold,” Annals of Probability, vol. 50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.","ama":"Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. 2022;50(2):591-648. doi:10.1214/21-AOP1541","apa":"Dello Schiavo, L. (2022). The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1541"},"title":"The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold","article_processing_charge":"No","external_id":{"isi":["000773518500005"],"arxiv":["1811.11598"]},"author":[{"full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"}],"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).","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","publication":"Annals of Probability","day":"01","year":"2022","isi":1,"date_created":"2022-05-08T22:01:44Z","date_published":"2022-03-01T00:00:00Z","doi":"10.1214/21-AOP1541","page":"591-648","_id":"11354","status":"public","article_type":"original","type":"journal_article","date_updated":"2023-10-17T12:50:24Z","department":[{"_id":"JaMa"}],"oa_version":"Preprint","abstract":[{"text":"We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.","lang":"eng"}],"intvolume":" 50","month":"03","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.1811.11598"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"ec_funded":1,"issue":"2","volume":50},{"year":"2021","day":"04","publication":"Communications in Information and Systems","page":"481-536","doi":"10.4310/CIS.2021.v21.n4.a1","date_published":"2021-06-04T00:00:00Z","date_created":"2021-09-19T08:53:19Z","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.","publisher":"International Press","quality_controlled":"1","oa":1,"citation":{"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.","chicago":"Karatzas, Ioannis, Jan Maas, and Walter Schachermayer. “Trajectorial Dissipation and Gradient Flow for the Relative Entropy in Markov Chains.” Communications in Information and Systems. International Press, 2021. https://doi.org/10.4310/CIS.2021.v21.n4.a1.","ieee":"I. Karatzas, J. Maas, and W. Schachermayer, “Trajectorial dissipation and gradient flow for the relative entropy in Markov chains,” Communications in Information and Systems, vol. 21, no. 4. International Press, pp. 481–536, 2021.","short":"I. Karatzas, J. Maas, W. Schachermayer, Communications in Information and Systems 21 (2021) 481–536.","apa":"Karatzas, I., Maas, J., & Schachermayer, W. (2021). Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. Communications in Information and Systems. International Press. https://doi.org/10.4310/CIS.2021.v21.n4.a1","ama":"Karatzas I, Maas J, Schachermayer W. Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. Communications in Information and Systems. 2021;21(4):481-536. doi:10.4310/CIS.2021.v21.n4.a1","mla":"Karatzas, Ioannis, et al. “Trajectorial Dissipation and Gradient Flow for the Relative Entropy in Markov Chains.” Communications in Information and Systems, vol. 21, no. 4, International Press, 2021, pp. 481–536, doi:10.4310/CIS.2021.v21.n4.a1."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","author":[{"last_name":"Karatzas","full_name":"Karatzas, Ioannis","first_name":"Ioannis"},{"orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Walter","full_name":"Schachermayer, Walter","last_name":"Schachermayer"}],"external_id":{"arxiv":["2005.14177"]},"article_processing_charge":"No","title":"Trajectorial dissipation and gradient flow for the relative entropy in Markov chains","project":[{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"publication_identifier":{"issn":["1526-7555"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"4","volume":21,"ec_funded":1,"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."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2005.14177"}],"month":"06","intvolume":" 21","date_updated":"2021-09-20T12:51:18Z","department":[{"_id":"JaMa"}],"_id":"10023","type":"journal_article","article_type":"original","status":"public","keyword":["Markov Chain","relative entropy","time reversal","steepest descent","gradient flow"]},{"date_updated":"2022-01-10T15:29:08Z","department":[{"_id":"JaMa"}],"_id":"10613","type":"journal_article","article_type":"original","keyword":["interacting particle systems","higher-order fields","hydrodynamic limit","equilibrium fluctuations","duality"],"status":"public","publication_status":"published","publication_identifier":{"issn":["1024-2953"]},"language":[{"iso":"eng"}],"ec_funded":1,"related_material":{"link":[{"relation":"other","url":"http://math-mprf.org/journal/articles/id1614/","description":"Link to Abstract on publisher's website"},{"description":"Referred to in Abstract","url":"https://arxiv.org/abs/2004.08412","relation":"used_for_analysis_in"}]},"issue":"3","volume":27,"abstract":[{"text":"Motivated by the recent preprint [\\emph{arXiv:2004.08412}] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher-order fields. Then, by considering the same class of infinite interacting particle systems as in [\\emph{arXiv:2004.08412}], namely symmetric simple exclusion and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\\emph{arXiv:2004.08412}], since we considered-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\\emph{arXiv:2004.08412}], since we consider a different notion of higher-order fluctuation fields.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/2008.13403","open_access":"1"}],"intvolume":" 27","month":"03","citation":{"ista":"Chen JP, Sau F. 2021. Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. Markov Processes And Related Fields. 27(3), 339–380.","chicago":"Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems.” Markov Processes And Related Fields. Polymat Publishing, 2021.","apa":"Chen, J. P., & Sau, F. (2021). Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. Markov Processes And Related Fields. Polymat Publishing.","ama":"Chen JP, Sau F. Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. Markov Processes And Related Fields. 2021;27(3):339-380.","ieee":"J. P. Chen and F. Sau, “Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems,” Markov Processes And Related Fields, vol. 27, no. 3. Polymat Publishing, pp. 339–380, 2021.","short":"J.P. Chen, F. Sau, Markov Processes And Related Fields 27 (2021) 339–380.","mla":"Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems.” Markov Processes And Related Fields, vol. 27, no. 3, Polymat Publishing, 2021, pp. 339–80."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","article_processing_charge":"No","external_id":{"arxiv":["2008.13403"]},"author":[{"first_name":"Joe P.","full_name":"Chen, Joe P.","last_name":"Chen"},{"id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico","last_name":"Sau","full_name":"Sau, Federico"}],"title":"Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"year":"2021","publication":"Markov Processes And Related Fields","day":"16","page":"339-380","date_created":"2022-01-10T14:02:31Z","date_published":"2021-03-16T00:00:00Z","acknowledgement":"F.S. would like to thank Mario Ayala and Frank Redig for useful discussions. J.P.C. acknowledges partial financial support from the US National Science Foundation (DMS-1855604). F.S. was financially supported by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.\r\n","oa":1,"publisher":"Polymat Publishing","quality_controlled":"1"},{"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"title":"Complete gradient estimates of quantum Markov semigroups","external_id":{"isi":["000691214200001"],"arxiv":["2007.13506"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior"},{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan","full_name":"Zhang, Haonan","last_name":"Zhang"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” Communications in Mathematical Physics, vol. 387, Springer Nature, 2021, pp. 761–791, doi:10.1007/s00220-021-04199-4.","ieee":"M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,” Communications in Mathematical Physics, vol. 387. Springer Nature, pp. 761–791, 2021.","short":"M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.","apa":"Wirth, M., & Zhang, H. (2021). Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04199-4","ama":"Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 2021;387:761–791. doi:10.1007/s00220-021-04199-4","chicago":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04199-4.","ista":"Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791."},"oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"Both authors would like to thank Jan Maas for fruitful discussions and helpful comments.","date_created":"2021-08-30T10:07:44Z","doi":"10.1007/s00220-021-04199-4","date_published":"2021-08-30T00:00:00Z","page":"761–791","publication":"Communications in Mathematical Physics","day":"30","year":"2021","has_accepted_license":"1","isi":1,"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"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)"},"type":"journal_article","article_type":"original","_id":"9973","department":[{"_id":"JaMa"}],"file_date_updated":"2021-09-08T09:46:34Z","ddc":["621"],"date_updated":"2023-08-11T11:09:07Z","intvolume":" 387","month":"08","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors.","lang":"eng"}],"ec_funded":1,"volume":387,"language":[{"iso":"eng"}],"file":[{"creator":"cchlebak","file_size":505971,"date_updated":"2021-09-08T09:46:34Z","file_name":"2021_CommunMathPhys_Wirth.pdf","date_created":"2021-09-08T07:34:24Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","checksum":"8a602f916b1c2b0dc1159708b7cb204b","file_id":"9990"}],"publication_status":"published","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]}},{"author":[{"first_name":"Simone","full_name":"Floreani, Simone","last_name":"Floreani"},{"full_name":"Redig, Frank","last_name":"Redig","first_name":"Frank"},{"id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico","full_name":"Sau, Federico","last_name":"Sau"}],"external_id":{"isi":["000697748500005"],"arxiv":["1911.12564"]},"article_processing_charge":"Yes","title":"Hydrodynamics for the partial exclusion process in random environment","citation":{"mla":"Floreani, Simone, et al. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” Stochastic Processes and Their Applications, vol. 142, Elsevier, 2021, pp. 124–58, doi:10.1016/j.spa.2021.08.006.","apa":"Floreani, S., Redig, F., & Sau, F. (2021). Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and Their Applications. Elsevier. https://doi.org/10.1016/j.spa.2021.08.006","ama":"Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 2021;142:124-158. doi:10.1016/j.spa.2021.08.006","ieee":"S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion process in random environment,” Stochastic Processes and their Applications, vol. 142. Elsevier, pp. 124–158, 2021.","short":"S. Floreani, F. Redig, F. Sau, Stochastic Processes and Their Applications 142 (2021) 124–158.","chicago":"Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” Stochastic Processes and Their Applications. Elsevier, 2021. https://doi.org/10.1016/j.spa.2021.08.006.","ista":"Floreani S, Redig F, Sau F. 2021. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 142, 124–158."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"page":"124-158","doi":"10.1016/j.spa.2021.08.006","date_published":"2021-08-27T00:00:00Z","date_created":"2021-09-19T22:01:25Z","isi":1,"has_accepted_license":"1","year":"2021","day":"27","publication":"Stochastic Processes and their Applications","publisher":"Elsevier","quality_controlled":"1","oa":1,"acknowledgement":"The authors would like to thank Marek Biskup and Alberto Chiarini for useful suggestions and Cristian Giardina, Frank den Hollander and Shubhamoy Nandan for inspiring discussions. S.F. acknowledges Simona Villa for her help in creating the picture. Furthermore, the authors thank two anonymous referees for the careful reading of the manuscript. S.F. acknowledges financial support from NWO, The Netherlands via the grant TOP1.17.019. F.S. acknowledges financial support from NWO via the TOP1 grant 613.001.552 as well as funding from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.","department":[{"_id":"JaMa"}],"file_date_updated":"2022-05-13T07:55:50Z","date_updated":"2023-08-14T06:52:43Z","ddc":["519"],"type":"journal_article","article_type":"original","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)"},"status":"public","keyword":["hydrodynamic limit","random environment","random conductance model","arbitrary starting point quenched invariance principle","duality","mild solution"],"_id":"10024","volume":142,"ec_funded":1,"publication_identifier":{"issn":["0304-4149"]},"publication_status":"published","file":[{"file_name":"2021_StochasticProcessesAppl_Floreani.pdf","date_created":"2022-05-13T07:55:50Z","file_size":2115791,"date_updated":"2022-05-13T07:55:50Z","creator":"dernst","success":1,"file_id":"11370","checksum":"56768c553d7218ee5714902ffec90ec4","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"08","intvolume":" 142","abstract":[{"text":"In this paper, we introduce a random environment for the exclusion process in obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we derive a quenched hydrodynamic limit in path space by strengthening the mild solution approach initiated in Nagy (2002) and Faggionato (2007). To this purpose, we prove, employing the technology developed for the random conductance model, a homogenization result in the form of an arbitrary starting point quenched invariance principle for a single particle in the same environment, which is a result of independent interest. The self-duality property of the partial exclusion process allows us to transfer this homogenization result to the particle system and, then, apply the tightness criterion in Redig et al. (2020).","lang":"eng"}],"oa_version":"Published Version"},{"date_updated":"2023-08-14T07:05:44Z","department":[{"_id":"JaMa"}],"_id":"10070","status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"publication_status":"published","volume":281,"issue":"11","ec_funded":1,"oa_version":"Preprint","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."}],"month":"09","intvolume":" 281","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2008.01492"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” Journal of Functional Analysis, vol. 281, no. 11, 109234, Elsevier, 2021, doi:10.1016/j.jfa.2021.109234.","ieee":"L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces,” Journal of Functional Analysis, vol. 281, no. 11. Elsevier, 2021.","short":"L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).","apa":"Dello Schiavo, L., & Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2021.109234","ama":"Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. 2021;281(11). doi:10.1016/j.jfa.2021.109234","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” Journal of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109234.","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."},"title":"Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces","author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870"},{"last_name":"Suzuki","full_name":"Suzuki, Kohei","first_name":"Kohei"}],"external_id":{"arxiv":["2008.01492"],"isi":["000703896600005"]},"article_processing_charge":"No","article_number":"109234","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"day":"15","publication":"Journal of Functional Analysis","isi":1,"year":"2021","doi":"10.1016/j.jfa.2021.109234","date_published":"2021-09-15T00:00:00Z","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.","publisher":"Elsevier","quality_controlled":"1","oa":1},{"department":[{"_id":"JaMa"}],"date_updated":"2023-08-17T07:12:05Z","type":"journal_article","article_type":"original","status":"public","_id":"9627","volume":64,"issue":"3","publication_status":"published","publication_identifier":{"issn":["0013-0915"],"eissn":["1464-3839"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1017/S0013091521000080"}],"scopus_import":"1","intvolume":" 64","month":"08","abstract":[{"text":"We compute the deficiency spaces of operators of the form 𝐻𝐴⊗̂ 𝐼+𝐼⊗̂ 𝐻𝐵, for symmetric 𝐻𝐴 and self-adjoint 𝐻𝐵. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301], but only proven under the restriction of 𝐻𝐵 having discrete, non-degenerate spectrum.","lang":"eng"}],"oa_version":"Published Version","external_id":{"isi":["000721363700003"],"arxiv":["1912.03670"]},"article_processing_charge":"No","author":[{"first_name":"Daniel","last_name":"Lenz","full_name":"Lenz, Daniel"},{"full_name":"Weinmann, Timon","last_name":"Weinmann","first_name":"Timon"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","first_name":"Melchior","last_name":"Wirth","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241"}],"title":"Self-adjoint extensions of bipartite Hamiltonians","citation":{"ista":"Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.","chicago":"Lenz, Daniel, Timon Weinmann, and Melchior Wirth. “Self-Adjoint Extensions of Bipartite Hamiltonians.” Proceedings of the Edinburgh Mathematical Society. Cambridge University Press, 2021. https://doi.org/10.1017/S0013091521000080.","short":"D. Lenz, T. Weinmann, M. Wirth, Proceedings of the Edinburgh Mathematical Society 64 (2021) 443–447.","ieee":"D. Lenz, T. Weinmann, and M. Wirth, “Self-adjoint extensions of bipartite Hamiltonians,” Proceedings of the Edinburgh Mathematical Society, vol. 64, no. 3. Cambridge University Press, pp. 443–447, 2021.","ama":"Lenz D, Weinmann T, Wirth M. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 2021;64(3):443-447. doi:10.1017/S0013091521000080","apa":"Lenz, D., Weinmann, T., & Wirth, M. (2021). Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. Cambridge University Press. https://doi.org/10.1017/S0013091521000080","mla":"Lenz, Daniel, et al. “Self-Adjoint Extensions of Bipartite Hamiltonians.” Proceedings of the Edinburgh Mathematical Society, vol. 64, no. 3, Cambridge University Press, 2021, pp. 443–47, doi:10.1017/S0013091521000080."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","page":"443-447","date_created":"2021-07-04T22:01:24Z","doi":"10.1017/S0013091521000080","date_published":"2021-08-01T00:00:00Z","year":"2021","isi":1,"publication":"Proceedings of the Edinburgh Mathematical Society","day":"01","oa":1,"quality_controlled":"1","publisher":"Cambridge University Press","acknowledgement":"M. W. gratefully acknowledges financial support by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes). T.W. thanks PAO Gazprom Neft, the Euler International Mathematical Institute in Saint Petersburg and ORISA GmbH for their financial support in the form of scholarships during his Master's and Bachelor's studies respectively. The authors want to thank Mark Malamud for pointing out the reference [1] to them. This work was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No 075-15-2019-1619."},{"type":"dissertation","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)"},"status":"public","_id":"10030","file_date_updated":"2022-03-10T12:14:42Z","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"supervisor":[{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas"}],"date_updated":"2023-09-07T13:31:06Z","ddc":["515"],"alternative_title":["ISTA Thesis"],"month":"09","acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"NanoFab"}],"abstract":[{"lang":"eng","text":"This PhD thesis is primarily focused on the study of discrete transport problems, introduced for the first time in the seminal works of Maas [Maa11] and Mielke [Mie11] on finite state Markov chains and reaction-diffusion equations, respectively. More in detail, my research focuses on the study of transport costs on graphs, in particular the convergence and the stability of such problems in the discrete-to-continuum limit. This thesis also includes some results concerning\r\nnon-commutative optimal transport. The first chapter of this thesis consists of a general introduction to the optimal transport problems, both in the discrete, the continuous, and the non-commutative setting. Chapters 2 and 3 present the content of two works, obtained in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have been able to show the convergence of discrete transport costs on periodic graphs to suitable continuous ones, which can be described by means of a homogenisation result. We first focus on the particular case of quadratic costs on the real line and then extending the result to more general costs in arbitrary dimension. Our results are the first complete characterisation of limits of transport costs on periodic graphs in arbitrary dimension which do not rely on any additional symmetry. In Chapter 4 we turn our attention to one of the intriguing connection between evolution equations and optimal transport, represented by the theory of gradient flows. We show that discrete gradient flow structures associated to a finite volume approximation of a certain class of diffusive equations (Fokker–Planck) is stable in the limit of vanishing meshes, reproving the convergence of the scheme via the method of evolutionary Γ-convergence and exploiting a more variational point of view on the problem. This is based on a collaboration with Dominik Forkert and Jan Maas. Chapter 5 represents a change of perspective, moving away from the discrete world and reaching the non-commutative one. As in the discrete case, we discuss how classical tools coming from the commutative optimal transport can be translated into the setting of density matrices. In particular, in this final chapter we present a non-commutative version of the Schrödinger problem (or entropic regularised optimal transport problem) and discuss existence and characterisation of minimisers, a duality result, and present a non-commutative version of the well-known Sinkhorn algorithm to compute the above mentioned optimisers. This is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally, Appendix A and B contain some additional material and discussions, with particular attention to Harnack inequalities and the regularity of flows on discrete spaces."}],"oa_version":"Published Version","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"10022"},{"relation":"part_of_dissertation","status":"public","id":"9792"},{"status":"public","id":"7573","relation":"part_of_dissertation"}]},"publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","degree_awarded":"PhD","file":[{"checksum":"8cd60dcb8762e8f21867e21e8001e183","file_id":"10032","access_level":"closed","relation":"source_file","content_type":"application/x-zip-compressed","date_created":"2021-09-21T09:17:34Z","file_name":"tex_and_pictures.zip","creator":"cchlebak","date_updated":"2022-03-10T12:14:42Z","file_size":3876668},{"checksum":"9789e9d967c853c1503ec7f307170279","file_id":"10047","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2021-09-27T11:14:31Z","file_name":"thesis_portinale_Final (1).pdf","date_updated":"2021-09-27T11:14:31Z","file_size":2532673,"creator":"cchlebak"}],"language":[{"iso":"eng"}],"project":[{"name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"author":[{"last_name":"Portinale","full_name":"Portinale, Lorenzo","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","title":"Discrete-to-continuum limits of transport problems and gradient flows in the space of measures","citation":{"apa":"Portinale, L. (2021). Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:10030","ama":"Portinale L. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. 2021. doi:10.15479/at:ista:10030","ieee":"L. Portinale, “Discrete-to-continuum limits of transport problems and gradient flows in the space of measures,” Institute of Science and Technology Austria, 2021.","short":"L. Portinale, Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures, Institute of Science and Technology Austria, 2021.","mla":"Portinale, Lorenzo. Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:10030.","ista":"Portinale L. 2021. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. Institute of Science and Technology Austria.","chicago":"Portinale, Lorenzo. “Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:10030."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publisher":"Institute of Science and Technology Austria","oa":1,"acknowledgement":"The author gratefully acknowledges support by the Austrian Science Fund (FWF), grants No W1245.","doi":"10.15479/at:ista:10030","date_published":"2021-09-22T00:00:00Z","date_created":"2021-09-21T09:14:15Z","has_accepted_license":"1","year":"2021","day":"22"},{"doi":"10.48550/arXiv.2106.11217","date_published":"2021-07-21T00:00:00Z","date_created":"2021-08-06T09:07:12Z","has_accepted_license":"1","year":"2021","day":"21","publication":"arXiv","oa":1,"acknowledgement":"This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors 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].","author":[{"id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","last_name":"Feliciangeli"},{"last_name":"Gerolin","full_name":"Gerolin, Augusto","first_name":"Augusto"},{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo","last_name":"Portinale","full_name":"Portinale, Lorenzo"}],"article_processing_charge":"No","external_id":{"arxiv":["2106.11217"]},"title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","citation":{"chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2106.11217.","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.” ArXiv, 2106.11217, doi:10.48550/arXiv.2106.11217.","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv. doi:10.48550/arXiv.2106.11217","apa":"Feliciangeli, D., Gerolin, A., & Portinale, L. (n.d.). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv. https://doi.org/10.48550/arXiv.2106.11217","short":"D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.).","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” arXiv. ."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"article_number":"2106.11217","related_material":{"record":[{"id":"9733","status":"public","relation":"dissertation_contains"},{"id":"10030","status":"public","relation":"dissertation_contains"},{"relation":"later_version","id":"12911","status":"public"}]},"ec_funded":1,"publication_status":"submitted","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"month":"07","abstract":[{"lang":"eng","text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on 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."}],"oa_version":"Preprint","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"date_updated":"2023-11-14T13:21:01Z","ddc":["510"],"type":"preprint","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)"},"status":"public","_id":"9792"},{"month":"08","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"license":"https://creativecommons.org/licenses/by-nd/4.0/","ec_funded":1,"related_material":{"record":[{"id":"9787","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"9792","status":"public"},{"id":"9225","status":"public","relation":"part_of_dissertation"},{"status":"public","id":"9781","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"9791"}]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"e88bb8ca43948abe060eb2d2fa719881","file_id":"9944","date_updated":"2021-09-06T09:28:56Z","file_size":1958710,"creator":"dfelicia","date_created":"2021-08-19T14:03:48Z","file_name":"Thesis_FeliciangeliA.pdf"},{"file_id":"9945","checksum":"72810843abee83705853505b3f8348aa","content_type":"application/octet-stream","relation":"source_file","access_level":"closed","file_name":"thesis.7z","date_created":"2021-08-19T14:06:35Z","file_size":3771669,"date_updated":"2022-03-10T12:13:57Z","creator":"dfelicia"}],"degree_awarded":"PhD","publication_status":"published","publication_identifier":{"issn":["2663-337X"]},"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","short":"CC BY-ND (4.0)"},"type":"dissertation","_id":"9733","department":[{"_id":"GradSch"},{"_id":"RoSe"},{"_id":"JaMa"}],"file_date_updated":"2022-03-10T12:13:57Z","ddc":["515","519","539"],"date_updated":"2024-03-06T12:30:44Z","supervisor":[{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas"}],"oa":1,"publisher":"Institute of Science and Technology Austria","date_created":"2021-07-27T15:48:30Z","doi":"10.15479/at:ista:9733","date_published":"2021-08-20T00:00:00Z","page":"180","day":"20","year":"2021","has_accepted_license":"1","project":[{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"title":"The polaron at strong coupling","article_processing_charge":"No","author":[{"id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","last_name":"Feliciangeli"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:9733.","ista":"Feliciangeli D. 2021. The polaron at strong coupling. Institute of Science and Technology Austria.","mla":"Feliciangeli, Dario. The Polaron at Strong Coupling. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:9733.","ieee":"D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and Technology Austria, 2021.","short":"D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and Technology Austria, 2021.","ama":"Feliciangeli D. The polaron at strong coupling. 2021. doi:10.15479/at:ista:9733","apa":"Feliciangeli, D. (2021). The polaron at strong coupling. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:9733"}},{"oa":1,"publisher":"Springer Nature","quality_controlled":"1","page":"319-378","date_created":"2019-04-30T07:34:18Z","date_published":"2020-01-01T00:00:00Z","doi":"10.1007/s10955-019-02434-w","year":"2020","isi":1,"has_accepted_license":"1","publication":"Journal of Statistical Physics","day":"01","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Di erential Systems","grant_number":" F06504","_id":"260482E2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"external_id":{"arxiv":["1811.04572"],"isi":["000498933300001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Eric A.","full_name":"Carlen, Eric A.","last_name":"Carlen"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan"}],"title":"Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems","citation":{"mla":"Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems.” Journal of Statistical Physics, vol. 178, no. 2, Springer Nature, 2020, pp. 319–78, doi:10.1007/s10955-019-02434-w.","ieee":"E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems,” Journal of Statistical Physics, vol. 178, no. 2. Springer Nature, pp. 319–378, 2020.","short":"E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378.","ama":"Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. Journal of Statistical Physics. 2020;178(2):319-378. doi:10.1007/s10955-019-02434-w","apa":"Carlen, E. A., & Maas, J. (2020). Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-019-02434-w","chicago":"Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems.” Journal of Statistical Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-019-02434-w.","ista":"Carlen EA, Maas J. 2020. Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. Journal of Statistical Physics. 178(2), 319–378."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","intvolume":" 178","month":"01","abstract":[{"lang":"eng","text":"We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates."}],"oa_version":"Published Version","ec_funded":1,"issue":"2","volume":178,"related_material":{"link":[{"url":"https://doi.org/10.1007/s10955-020-02671-4","relation":"erratum"}]},"publication_status":"published","publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"language":[{"iso":"eng"}],"file":[{"checksum":"7b04befbdc0d4982c0ee945d25d19872","file_id":"7209","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2019_JourStatistPhysics_Carlen.pdf","date_created":"2019-12-23T12:03:09Z","creator":"dernst","file_size":905538,"date_updated":"2020-07-14T12:47:28Z"}],"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)"},"article_type":"original","type":"journal_article","status":"public","_id":"6358","file_date_updated":"2020-07-14T12:47:28Z","department":[{"_id":"JaMa"}],"date_updated":"2023-08-17T13:49:40Z","ddc":["500"]},{"_id":"74","series_title":"LNM","status":"public","type":"book_chapter","date_updated":"2023-08-17T13:48:31Z","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"intvolume":" 2256","month":"06","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.07350"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eisbn":["9783030360207"],"issn":["00758434"],"eissn":["16179692"],"isbn":["9783030360191"]},"ec_funded":1,"volume":2256,"project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” In Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-36020-7_1.","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.","mla":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer Nature, 2020, pp. 1–27, doi:10.1007/978-3-030-36020-7_1.","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27.","ieee":"A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures,” in Geometric Aspects of Functional Analysis, vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.","ama":"Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Klartag B, Milman E, eds. Geometric Aspects of Functional Analysis. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:10.1007/978-3-030-36020-7_1","apa":"Akopyan, A., & Karasev, R. (2020). Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In B. Klartag & E. Milman (Eds.), Geometric Aspects of Functional Analysis (Vol. 2256, pp. 1–27). Springer Nature. https://doi.org/10.1007/978-3-030-36020-7_1"},"title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","editor":[{"first_name":"Bo'az","full_name":"Klartag, Bo'az","last_name":"Klartag"},{"first_name":"Emanuel","full_name":"Milman, Emanuel","last_name":"Milman"}],"external_id":{"arxiv":["1808.07350"],"isi":["000557689300003"]},"article_processing_charge":"No","author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"oa":1,"quality_controlled":"1","publisher":"Springer Nature","publication":"Geometric Aspects of Functional Analysis","day":"21","year":"2020","isi":1,"date_created":"2018-12-11T11:44:29Z","date_published":"2020-06-21T00:00:00Z","doi":"10.1007/978-3-030-36020-7_1","page":"1-27"},{"title":"Nondivergence form quasilinear heat equations driven by space-time white noise","author":[{"first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87","full_name":"Gerencser, Mate","last_name":"Gerencser"}],"external_id":{"isi":["000531049800007"],"arxiv":["1902.07635"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"short":"M. Gerencser, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 37 (2020) 663–682.","ieee":"M. Gerencser, “Nondivergence form quasilinear heat equations driven by space-time white noise,” Annales de l’Institut Henri Poincaré C, Analyse non linéaire, vol. 37, no. 3. Elsevier, pp. 663–682, 2020.","ama":"Gerencser M. Nondivergence form quasilinear heat equations driven by space-time white noise. Annales de l’Institut Henri Poincaré C, Analyse non linéaire. 2020;37(3):663-682. doi:10.1016/j.anihpc.2020.01.003","apa":"Gerencser, M. (2020). Nondivergence form quasilinear heat equations driven by space-time white noise. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire. Elsevier. https://doi.org/10.1016/j.anihpc.2020.01.003","mla":"Gerencser, Mate. “Nondivergence Form Quasilinear Heat Equations Driven by Space-Time White Noise.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, vol. 37, no. 3, Elsevier, 2020, pp. 663–82, doi:10.1016/j.anihpc.2020.01.003.","ista":"Gerencser M. 2020. Nondivergence form quasilinear heat equations driven by space-time white noise. Annales de l’Institut Henri Poincaré C, Analyse non linéaire. 37(3), 663–682.","chicago":"Gerencser, Mate. “Nondivergence Form Quasilinear Heat Equations Driven by Space-Time White Noise.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire. Elsevier, 2020. https://doi.org/10.1016/j.anihpc.2020.01.003."},"quality_controlled":"1","publisher":"Elsevier","oa":1,"doi":"10.1016/j.anihpc.2020.01.003","date_published":"2020-05-01T00:00:00Z","date_created":"2020-01-29T09:39:41Z","page":"663-682","day":"01","publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","isi":1,"year":"2020","status":"public","type":"journal_article","article_type":"original","_id":"7388","department":[{"_id":"JaMa"}],"date_updated":"2023-08-17T14:35:46Z","month":"05","intvolume":" 37","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.07635"}],"oa_version":"Preprint","abstract":[{"text":"We give a Wong-Zakai type characterisation of the solutions of quasilinear heat equations driven by space-time white noise in 1 + 1 dimensions. In order to show that the renormalisation counterterms are local in the solution, a careful arrangement of a few hundred terms is required. The main tool in this computation is a general ‘integration by parts’ formula that provides a number of linear identities for the renormalisation constants.","lang":"eng"}],"volume":37,"issue":"3","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0294-1449"]},"publication_status":"published"},{"acknowledgement":"The author would like to thank Quanhua Xu, Adam Skalski, Ke Li and Zhi Yin for their valuable comments. He also would like to thank the anonymous referees for pointing out some errors in an earlier version of this paper and for helpful comments and suggestions that make this paper better. The research was partially supported by the NCN (National Centre of Science) grant 2014/14/E/ST1/00525, the French project ISITE-BFC (contract ANR-15-IDEX-03), NSFC No. 11826012, and the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411.","publisher":"Elsevier","quality_controlled":"1","oa":1,"isi":1,"year":"2020","day":"13","publication":"Advances in Mathematics","date_published":"2020-05-13T00:00:00Z","doi":"10.1016/j.aim.2020.107053","date_created":"2020-02-23T21:43:50Z","article_number":"107053","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"citation":{"ista":"Zhang H. 2020. From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics. 365, 107053.","chicago":"Zhang, Haonan. “From Wigner-Yanase-Dyson Conjecture to Carlen-Frank-Lieb Conjecture.” Advances in Mathematics. Elsevier, 2020. https://doi.org/10.1016/j.aim.2020.107053.","ieee":"H. Zhang, “From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture,” Advances in Mathematics, vol. 365. Elsevier, 2020.","short":"H. Zhang, Advances in Mathematics 365 (2020).","ama":"Zhang H. From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics. 2020;365. doi:10.1016/j.aim.2020.107053","apa":"Zhang, H. (2020). From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2020.107053","mla":"Zhang, Haonan. “From Wigner-Yanase-Dyson Conjecture to Carlen-Frank-Lieb Conjecture.” Advances in Mathematics, vol. 365, 107053, Elsevier, 2020, doi:10.1016/j.aim.2020.107053."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan","full_name":"Zhang, Haonan","last_name":"Zhang"}],"article_processing_charge":"No","external_id":{"arxiv":["1811.01205"],"isi":["000522798000001"]},"title":"From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture","abstract":[{"lang":"eng","text":"In this paper we study the joint convexity/concavity of the trace functions Ψp,q,s(A,B)=Tr(Bq2K∗ApKBq2)s, p,q,s∈R,\r\nwhere A and B are positive definite matrices and K is any fixed invertible matrix. We will give full range of (p,q,s)∈R3 for Ψp,q,s to be jointly convex/concave for all K. As a consequence, we confirm a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture of Audenaert and Datta and obtain the full range of (α,z) for α-z Rényi relative entropies to be monotone under completely positive trace preserving maps. We also give simpler proofs of many known results, including the concavity of Ψp,0,1/p for 0
Journal of Mathematical Physics. AIP Publishing, 2020. https://doi.org/10.1063/5.0022787.","ista":"Zhang H. 2020. Equality conditions of data processing inequality for α-z Rényi relative entropies. Journal of Mathematical Physics. 61(10), 102201.","mla":"Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z Rényi Relative Entropies.” Journal of Mathematical Physics, vol. 61, no. 10, 102201, AIP Publishing, 2020, doi:10.1063/5.0022787.","ieee":"H. Zhang, “Equality conditions of data processing inequality for α-z Rényi relative entropies,” Journal of Mathematical Physics, vol. 61, no. 10. AIP Publishing, 2020.","short":"H. Zhang, Journal of Mathematical Physics 61 (2020).","ama":"Zhang H. Equality conditions of data processing inequality for α-z Rényi relative entropies. Journal of Mathematical Physics. 2020;61(10). doi:10.1063/5.0022787","apa":"Zhang, H. (2020). Equality conditions of data processing inequality for α-z Rényi relative entropies. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0022787"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"external_id":{"arxiv":["2004.02831"],"isi":["000587107200002"]},"article_processing_charge":"No","author":[{"last_name":"Maas","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"},{"full_name":"Mielke, Alexander","last_name":"Mielke","first_name":"Alexander"}],"title":"Modeling of chemical reaction systems with detailed balance using gradient structures","citation":{"apa":"Maas, J., & Mielke, A. (2020). Modeling of chemical reaction systems with detailed balance using gradient structures. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-020-02663-4","ama":"Maas J, Mielke A. Modeling of chemical reaction systems with detailed balance using gradient structures. Journal of Statistical Physics. 2020;181(6):2257-2303. doi:10.1007/s10955-020-02663-4","short":"J. Maas, A. Mielke, Journal of Statistical Physics 181 (2020) 2257–2303.","ieee":"J. Maas and A. Mielke, “Modeling of chemical reaction systems with detailed balance using gradient structures,” Journal of Statistical Physics, vol. 181, no. 6. Springer Nature, pp. 2257–2303, 2020.","mla":"Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” Journal of Statistical Physics, vol. 181, no. 6, Springer Nature, 2020, pp. 2257–303, doi:10.1007/s10955-020-02663-4.","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.","chicago":"Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” Journal of Statistical Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-020-02663-4."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":" F06504","name":"Taming Complexity in Partial Di erential Systems","_id":"260482E2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"page":"2257-2303","date_created":"2020-11-15T23:01:18Z","doi":"10.1007/s10955-020-02663-4","date_published":"2020-12-01T00:00:00Z","year":"2020","has_accepted_license":"1","isi":1,"publication":"Journal of Statistical Physics","day":"01","oa":1,"publisher":"Springer Nature","quality_controlled":"1","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).","file_date_updated":"2021-02-04T10:29:11Z","department":[{"_id":"JaMa"}],"date_updated":"2023-08-22T13:24:27Z","ddc":["510"],"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)"},"article_type":"original","type":"journal_article","status":"public","_id":"8758","ec_funded":1,"issue":"6","volume":181,"publication_status":"published","publication_identifier":{"issn":["00224715"],"eissn":["15729613"]},"language":[{"iso":"eng"}],"file":[{"file_size":753596,"date_updated":"2021-02-04T10:29:11Z","creator":"dernst","file_name":"2020_JourStatPhysics_Maas.pdf","date_created":"2021-02-04T10:29:11Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"9087","checksum":"bc2b63a90197b97cbc73eccada4639f5"}],"scopus_import":"1","intvolume":" 181","month":"12","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"}],"oa_version":"Published Version"},{"project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"citation":{"apa":"Forkert, D. L. (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. https://doi.org/10.15479/AT:ISTA:7629","ama":"Forkert DL. Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains. 2020. doi:10.15479/AT:ISTA:7629","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.","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.","mla":"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, doi:10.15479/AT:ISTA:7629.","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.","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. https://doi.org/10.15479/AT:ISTA:7629."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","author":[{"full_name":"Forkert, Dominik L","last_name":"Forkert","first_name":"Dominik L","id":"35C79D68-F248-11E8-B48F-1D18A9856A87"}],"title":"Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains","oa":1,"publisher":"Institute of Science and Technology Austria","year":"2020","has_accepted_license":"1","day":"31","page":"154","date_created":"2020-04-02T06:40:23Z","date_published":"2020-03-31T00:00:00Z","doi":"10.15479/AT:ISTA:7629","_id":"7629","type":"dissertation","status":"public","date_updated":"2023-09-07T13:03:12Z","supervisor":[{"first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas"}],"ddc":["510"],"file_date_updated":"2020-07-14T12:48:01Z","department":[{"_id":"JaMa"}],"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","alternative_title":["ISTA Thesis"],"month":"03","degree_awarded":"PhD","publication_status":"published","publication_identifier":{"issn":["2663-337X"]},"language":[{"iso":"eng"}],"file":[{"file_name":"Thesis_Forkert_PDFA.pdf","date_created":"2020-04-14T10:47:59Z","file_size":3297129,"date_updated":"2020-07-14T12:48:01Z","creator":"dernst","checksum":"c814a1a6195269ca6fe48b0dca45ae8a","file_id":"7657","content_type":"application/pdf","relation":"main_file","access_level":"open_access"},{"date_created":"2020-04-14T10:47:59Z","file_name":"Thesis_Forkert_source.zip","date_updated":"2020-07-14T12:48:01Z","file_size":1063908,"creator":"dernst","checksum":"ceafb53f923d1b5bdf14b2b0f22e4a81","file_id":"7658","content_type":"application/x-zip-compressed","access_level":"closed","relation":"source_file"}],"ec_funded":1},{"month":"07","intvolume":" 139","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1905.05757","open_access":"1"}],"oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"issue":"7","volume":139,"related_material":{"record":[{"status":"public","id":"10030","relation":"dissertation_contains"}]},"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["00217824"]},"publication_status":"published","status":"public","type":"journal_article","article_type":"original","_id":"7573","department":[{"_id":"JaMa"}],"date_updated":"2023-09-07T13:31:05Z","publisher":"Elsevier","quality_controlled":"1","oa":1,"acknowledgement":"J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 716117). J.M. and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 350398276.","date_published":"2020-07-01T00:00:00Z","doi":"10.1016/j.matpur.2020.02.008","date_created":"2020-03-08T23:00:47Z","page":"204-234","day":"01","publication":"Journal de Mathematiques Pures et Appliquees","isi":1,"year":"2020","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"name":"Taming Complexity in Partial Di erential Systems","grant_number":" F06504","_id":"260482E2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations"}],"title":"Homogenisation of one-dimensional discrete optimal transport","author":[{"last_name":"Gladbach","full_name":"Gladbach, Peter","first_name":"Peter"},{"first_name":"Eva","full_name":"Kopfer, Eva","last_name":"Kopfer"},{"last_name":"Maas","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"},{"full_name":"Portinale, Lorenzo","last_name":"Portinale","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo"}],"article_processing_charge":"No","external_id":{"arxiv":["1905.05757"],"isi":["000539439400008"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of One-Dimensional Discrete Optimal Transport.” Journal de Mathematiques Pures et Appliquees. Elsevier, 2020. https://doi.org/10.1016/j.matpur.2020.02.008.","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.","mla":"Gladbach, Peter, et al. “Homogenisation of One-Dimensional Discrete Optimal Transport.” Journal de Mathematiques Pures et Appliquees, vol. 139, no. 7, Elsevier, 2020, pp. 204–34, doi:10.1016/j.matpur.2020.02.008.","ieee":"P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of one-dimensional discrete optimal transport,” Journal de Mathematiques Pures et Appliquees, vol. 139, no. 7. Elsevier, pp. 204–234, 2020.","short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Journal de Mathematiques Pures et Appliquees 139 (2020) 204–234.","apa":"Gladbach, P., Kopfer, E., Maas, J., & Portinale, L. (2020). Homogenisation of one-dimensional discrete optimal transport. Journal de Mathematiques Pures et Appliquees. Elsevier. https://doi.org/10.1016/j.matpur.2020.02.008","ama":"Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of one-dimensional discrete optimal transport. Journal de Mathematiques Pures et Appliquees. 2020;139(7):204-234. doi:10.1016/j.matpur.2020.02.008"}},{"publication_status":"submitted","year":"2020","language":[{"iso":"eng"}],"publication":"arXiv","day":"25","page":"33","date_created":"2021-09-17T10:57:27Z","ec_funded":1,"date_published":"2020-08-25T00:00:00Z","related_material":{"record":[{"id":"11739","status":"public","relation":"later_version"},{"id":"10030","status":"public","relation":"dissertation_contains"}]},"abstract":[{"lang":"eng","text":"We consider finite-volume approximations of Fokker-Planck equations on bounded convex domains in 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 Γ-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalising 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."}],"acknowledgement":"This work is supported 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), grants No F65 and W1245.","oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/2008.10962","open_access":"1"}],"oa":1,"month":"08","citation":{"ama":"Forkert DL, Maas J, Portinale L. Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. arXiv.","apa":"Forkert, D. L., Maas, J., & Portinale, L. (n.d.). Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. arXiv.","short":"D.L. Forkert, J. Maas, L. Portinale, ArXiv (n.d.).","ieee":"D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” arXiv. .","mla":"Forkert, Dominik L., et al. “Evolutionary Γ-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” ArXiv, 2008.10962.","ista":"Forkert DL, Maas J, Portinale L. Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. arXiv, 2008.10962.","chicago":"Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary Γ-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” ArXiv, n.d."},"date_updated":"2023-09-07T13:31:05Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","external_id":{"arxiv":["2008.10962"]},"article_processing_charge":"No","author":[{"last_name":"Forkert","full_name":"Forkert, Dominik L","id":"35C79D68-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik L"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan"},{"full_name":"Portinale, Lorenzo","last_name":"Portinale","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"}],"title":"Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions","department":[{"_id":"JaMa"}],"_id":"10022","article_number":"2008.10962","type":"preprint","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"status":"public"},{"citation":{"chicago":"Gladbach, Peter, Eva Kopfer, and Jan Maas. “Scaling Limits of Discrete Optimal Transport.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2020. https://doi.org/10.1137/19M1243440.","ista":"Gladbach P, Kopfer E, Maas J. 2020. Scaling limits of discrete optimal transport. SIAM Journal on Mathematical Analysis. 52(3), 2759–2802.","mla":"Gladbach, Peter, et al. “Scaling Limits of Discrete Optimal Transport.” SIAM Journal on Mathematical Analysis, vol. 52, no. 3, Society for Industrial and Applied Mathematics, 2020, pp. 2759–802, doi:10.1137/19M1243440.","ama":"Gladbach P, Kopfer E, Maas J. Scaling limits of discrete optimal transport. SIAM Journal on Mathematical Analysis. 2020;52(3):2759-2802. doi:10.1137/19M1243440","apa":"Gladbach, P., Kopfer, E., & Maas, J. (2020). Scaling limits of discrete optimal transport. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1243440","ieee":"P. Gladbach, E. Kopfer, and J. Maas, “Scaling limits of discrete optimal transport,” SIAM Journal on Mathematical Analysis, vol. 52, no. 3. Society for Industrial and Applied Mathematics, pp. 2759–2802, 2020.","short":"P. Gladbach, E. Kopfer, J. Maas, SIAM Journal on Mathematical Analysis 52 (2020) 2759–2802."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"arxiv":["1809.01092"],"isi":["000546975100017"]},"article_processing_charge":"No","author":[{"last_name":"Gladbach","full_name":"Gladbach, Peter","first_name":"Peter"},{"first_name":"Eva","full_name":"Kopfer, Eva","last_name":"Kopfer"},{"last_name":"Maas","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"}],"publist_id":"7983","title":"Scaling limits of discrete optimal transport","year":"2020","isi":1,"publication":"SIAM Journal on Mathematical Analysis","day":"01","page":"2759-2802","date_created":"2018-12-11T11:44:28Z","doi":"10.1137/19M1243440","date_published":"2020-10-01T00:00:00Z","oa":1,"quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics","date_updated":"2023-09-18T08:13:15Z","department":[{"_id":"JaMa"}],"_id":"71","type":"journal_article","article_type":"original","status":"public","publication_status":"published","publication_identifier":{"issn":["00361410"],"eissn":["10957154"]},"language":[{"iso":"eng"}],"issue":"3","volume":52,"abstract":[{"text":"We consider dynamical transport metrics for probability measures on discretisations of a bounded convex domain in ℝd. These metrics are natural discrete counterparts to the Kantorovich metric 𝕎2, defined using a Benamou-Brenier type formula. Under mild assumptions we prove an asymptotic upper bound for the discrete transport metric Wt in terms of 𝕎2, as the size of the mesh T tends to 0. However, we show that the corresponding lower bound may fail in general, even on certain one-dimensional and symmetric two-dimensional meshes. In addition, we show that the asymptotic lower bound holds under an isotropy assumption on the mesh, which turns out to be essentially necessary. This assumption is satisfied, e.g., for tilings by convex regular polygons, and it implies Gromov-Hausdorff convergence of the transport metric.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1809.01092","open_access":"1"}],"scopus_import":"1","intvolume":" 52","month":"10"},{"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"day":"16","publication":"Electronic Journal of Probability","has_accepted_license":"1","isi":1,"year":"2020","doi":"10.1214/20-EJP479","date_published":"2020-07-16T00:00:00Z","date_created":"2019-04-30T07:40:17Z","article_number":"82","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"K. Dareiotis, M. Gerencser, Electronic Journal of Probability 25 (2020).","ieee":"K. Dareiotis and M. Gerencser, “On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift,” Electronic Journal of Probability, vol. 25. Institute of Mathematical Statistics, 2020.","apa":"Dareiotis, K., & Gerencser, M. (2020). On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/20-EJP479","ama":"Dareiotis K, Gerencser M. On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. 2020;25. doi:10.1214/20-EJP479","mla":"Dareiotis, Konstantinos, and Mate Gerencser. “On the Regularisation of the Noise for the Euler-Maruyama Scheme with Irregular Drift.” Electronic Journal of Probability, vol. 25, 82, Institute of Mathematical Statistics, 2020, doi:10.1214/20-EJP479.","ista":"Dareiotis K, Gerencser M. 2020. On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. 25, 82.","chicago":"Dareiotis, Konstantinos, and Mate Gerencser. “On the Regularisation of the Noise for the Euler-Maruyama Scheme with Irregular Drift.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/20-EJP479."},"title":"On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift","author":[{"full_name":"Dareiotis, Konstantinos","last_name":"Dareiotis","first_name":"Konstantinos"},{"first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87","last_name":"Gerencser","full_name":"Gerencser, Mate"}],"article_processing_charge":"No","external_id":{"isi":["000550150700001"],"arxiv":["1812.04583"]},"oa_version":"Published Version","abstract":[{"text":"The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of α-Hölder drift in the recent literature the rate α/2 was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to 1/2 for all α>0. The result extends to Dini continuous coefficients, while in d=1 also to all bounded measurable coefficients.","lang":"eng"}],"month":"07","intvolume":" 25","scopus_import":"1","file":[{"success":1,"file_id":"8549","checksum":"8e7c42e72596f6889d786e8e8b89994f","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2020_EJournProbab_Dareiotis.pdf","date_created":"2020-09-21T13:15:02Z","file_size":273042,"date_updated":"2020-09-21T13:15:02Z","creator":"dernst"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1083-6489"]},"publication_status":"published","volume":25,"_id":"6359","status":"public","article_type":"original","type":"journal_article","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)"},"ddc":["510"],"date_updated":"2023-10-16T09:22:50Z","department":[{"_id":"JaMa"}],"file_date_updated":"2020-09-21T13:15:02Z"},{"_id":"8973","status":"public","type":"journal_article","article_type":"original","ddc":["510"],"date_updated":"2023-10-17T12:51:56Z","department":[{"_id":"JaMa"}],"file_date_updated":"2020-12-28T08:24:08Z","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider the symmetric simple exclusion process in Zd with quenched bounded dynamic random conductances and prove its hydrodynamic limit in path space. The main tool is the connection, due to the self-duality of the process, between the invariance principle for single particles starting from all points and the macroscopic behavior of the density field. While the hydrodynamic limit at fixed macroscopic times is obtained via a generalization to the time-inhomogeneous context of the strategy introduced in [41], in order to prove tightness for the sequence of empirical density fields we develop a new criterion based on the notion of uniform conditional stochastic continuity, following [50]. In conclusion, we show that uniform elliptic dynamic conductances provide an example of environments in which the so-called arbitrary starting point invariance principle may be derived from the invariance principle of a single particle starting from the origin. Therefore, our hydrodynamics result applies to the examples of quenched environments considered in, e.g., [1], [3], [6] in combination with the hypothesis of uniform ellipticity."}],"month":"10","intvolume":" 25","scopus_import":"1","file":[{"creator":"dernst","date_updated":"2020-12-28T08:24:08Z","file_size":696653,"date_created":"2020-12-28T08:24:08Z","file_name":"2020_ElectronJProbab_Redig.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"d75359b9814e78d57c0a481b7cde3751","file_id":"8976","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1083-6489"]},"publication_status":"published","volume":25,"ec_funded":1,"article_number":"138","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Redig, Frank, et al. “Symmetric Simple Exclusion Process in Dynamic Environment: Hydrodynamics.” Electronic Journal of Probability, vol. 25, 138, Institute of Mathematical Statistics, 2020, doi:10.1214/20-EJP536.","short":"F. Redig, E. Saada, F. Sau, Electronic Journal of Probability 25 (2020).","ieee":"F. Redig, E. Saada, and F. Sau, “Symmetric simple exclusion process in dynamic environment: Hydrodynamics,” Electronic Journal of Probability, vol. 25. Institute of Mathematical Statistics, 2020.","apa":"Redig, F., Saada, E., & Sau, F. (2020). Symmetric simple exclusion process in dynamic environment: Hydrodynamics. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/20-EJP536","ama":"Redig F, Saada E, Sau F. Symmetric simple exclusion process in dynamic environment: Hydrodynamics. Electronic Journal of Probability. 2020;25. doi:10.1214/20-EJP536","chicago":"Redig, Frank, Ellen Saada, and Federico Sau. “Symmetric Simple Exclusion Process in Dynamic Environment: Hydrodynamics.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/20-EJP536.","ista":"Redig F, Saada E, Sau F. 2020. Symmetric simple exclusion process in dynamic environment: Hydrodynamics. Electronic Journal of Probability. 25, 138."},"title":"Symmetric simple exclusion process in dynamic environment: Hydrodynamics","author":[{"last_name":"Redig","full_name":"Redig, Frank","first_name":"Frank"},{"full_name":"Saada, Ellen","last_name":"Saada","first_name":"Ellen"},{"first_name":"Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425","full_name":"Sau, Federico","last_name":"Sau"}],"external_id":{"isi":["000591737500001"],"arxiv":["1811.01366"]},"article_processing_charge":"No","acknowledgement":"We warmly thank S.R.S. Varadhan for many enlightening discussions at an early stage of this work. We are indebted to Francesca Collet for fruitful discussions and constant support all throughout this work. We thank Simone Floreani\r\nand Alberto Chiarini for helpful conversations on the final part of this paper as well as both referees for their careful reading and for raising relevant issues on some weak points contained in a previous version of this manuscript; we believe this helped us to improve it.\r\nPart of this work was done during the authors’ stay at the Institut Henri Poincaré (UMS 5208 CNRS-Sorbonne Université) – Centre Emile Borel during the trimester Stochastic Dynamics Out of Equilibrium. The authors thank this institution for hospitality and support (through LabEx CARMIN, ANR-10-LABX-59-01). F.S. thanks laboratoire\r\nMAP5 of Université de Paris, and E.S. thanks Delft University, for financial support and hospitality. F.S. acknowledges NWO for financial support via the TOP1 grant 613.001.552 as well as funding from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411. This research has been conducted within the FP2M federation (CNRS FR 2036).","quality_controlled":"1","publisher":" Institute of Mathematical Statistics","oa":1,"day":"21","publication":"Electronic Journal of Probability","has_accepted_license":"1","isi":1,"year":"2020","date_published":"2020-10-21T00:00:00Z","doi":"10.1214/20-EJP536","date_created":"2020-12-27T23:01:17Z"},{"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1910.10050","open_access":"1"}],"intvolume":" 28","month":"10","abstract":[{"lang":"eng","text":"We consider an optimal control problem for an abstract nonlinear dissipative evolution equation. The differential constraint is penalized by augmenting the target functional by a nonnegative global-in-time functional which is null-minimized in the evolution equation is satisfied. Different variational settings are presented, leading to the convergence of the penalization method for gradient flows, noncyclic and semimonotone flows, doubly nonlinear evolutions, and GENERIC systems. "}],"oa_version":"Preprint","issue":"2","volume":28,"publication_status":"published","publication_identifier":{"issn":["1343-4373"]},"language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","status":"public","_id":"7550","department":[{"_id":"JaMa"}],"date_updated":"2022-06-17T07:52:41Z","oa":1,"publisher":"Gakko Tosho","quality_controlled":"1","acknowledgement":"This work is supported by Vienna Science and Technology Fund (WWTF) through Project MA14-009 and by the Austrian Science Fund (FWF) projects F 65 and I 2375.","page":"425-447","date_created":"2020-02-28T10:54:41Z","date_published":"2019-10-22T00:00:00Z","year":"2019","publication":"Advances in Mathematical Sciences and Applications","day":"22","project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"external_id":{"arxiv":["1910.10050"]},"article_processing_charge":"No","author":[{"last_name":"Portinale","full_name":"Portinale, Lorenzo","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Ulisse","full_name":"Stefanelli, Ulisse","last_name":"Stefanelli"}],"title":"Penalization via global functionals of optimal-control problems for dissipative evolution","citation":{"mla":"Portinale, Lorenzo, and Ulisse Stefanelli. “Penalization via Global Functionals of Optimal-Control Problems for Dissipative Evolution.” Advances in Mathematical Sciences and Applications, vol. 28, no. 2, Gakko Tosho, 2019, pp. 425–47.","ieee":"L. Portinale and U. Stefanelli, “Penalization via global functionals of optimal-control problems for dissipative evolution,” Advances in Mathematical Sciences and Applications, vol. 28, no. 2. Gakko Tosho, pp. 425–447, 2019.","short":"L. Portinale, U. Stefanelli, Advances in Mathematical Sciences and Applications 28 (2019) 425–447.","apa":"Portinale, L., & Stefanelli, U. (2019). Penalization via global functionals of optimal-control problems for dissipative evolution. Advances in Mathematical Sciences and Applications. Gakko Tosho.","ama":"Portinale L, Stefanelli U. Penalization via global functionals of optimal-control problems for dissipative evolution. Advances in Mathematical Sciences and Applications. 2019;28(2):425-447.","chicago":"Portinale, Lorenzo, and Ulisse Stefanelli. “Penalization via Global Functionals of Optimal-Control Problems for Dissipative Evolution.” Advances in Mathematical Sciences and Applications. Gakko Tosho, 2019.","ista":"Portinale L, Stefanelli U. 2019. Penalization via global functionals of optimal-control problems for dissipative evolution. Advances in Mathematical Sciences and Applications. 28(2), 425–447."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"date_updated":"2023-08-24T14:20:49Z","department":[{"_id":"JaMa"}],"_id":"301","status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","volume":129,"issue":"3","oa_version":"Preprint","abstract":[{"text":"A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that appear in the usual formulation are not even defined in the Itô sense.","lang":"eng"}],"month":"03","intvolume":" 129","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1611.04177"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"apa":"Gerencser, M., & Gyöngy, I. (2019). A Feynman–Kac formula for stochastic Dirichlet problems. Stochastic Processes and Their Applications. Elsevier. https://doi.org/10.1016/j.spa.2018.04.003","ama":"Gerencser M, Gyöngy I. A Feynman–Kac formula for stochastic Dirichlet problems. Stochastic Processes and their Applications. 2019;129(3):995-1012. doi:10.1016/j.spa.2018.04.003","short":"M. Gerencser, I. Gyöngy, Stochastic Processes and Their Applications 129 (2019) 995–1012.","ieee":"M. Gerencser and I. Gyöngy, “A Feynman–Kac formula for stochastic Dirichlet problems,” Stochastic Processes and their Applications, vol. 129, no. 3. Elsevier, pp. 995–1012, 2019.","mla":"Gerencser, Mate, and István Gyöngy. “A Feynman–Kac Formula for Stochastic Dirichlet Problems.” Stochastic Processes and Their Applications, vol. 129, no. 3, Elsevier, 2019, pp. 995–1012, doi:10.1016/j.spa.2018.04.003.","ista":"Gerencser M, Gyöngy I. 2019. A Feynman–Kac formula for stochastic Dirichlet problems. Stochastic Processes and their Applications. 129(3), 995–1012.","chicago":"Gerencser, Mate, and István Gyöngy. “A Feynman–Kac Formula for Stochastic Dirichlet Problems.” Stochastic Processes and Their Applications. Elsevier, 2019. https://doi.org/10.1016/j.spa.2018.04.003."},"title":"A Feynman–Kac formula for stochastic Dirichlet problems","author":[{"full_name":"Gerencser, Mate","last_name":"Gerencser","first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Gyöngy, István","last_name":"Gyöngy","first_name":"István"}],"external_id":{"isi":["000458945300012"],"arxiv":["1611.04177"]},"article_processing_charge":"No","day":"01","publication":"Stochastic Processes and their Applications","isi":1,"year":"2019","date_published":"2019-03-01T00:00:00Z","doi":"10.1016/j.spa.2018.04.003","date_created":"2018-12-11T11:45:42Z","page":"995-1012","quality_controlled":"1","publisher":"Elsevier","oa":1},{"article_type":"original","type":"journal_article","status":"public","_id":"65","department":[{"_id":"JaMa"}],"date_updated":"2023-08-24T14:30:16Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1803.06953"}],"scopus_import":"1","intvolume":" 266","month":"03","abstract":[{"lang":"eng","text":"We provide an entropy formulation for porous medium-type equations with a stochastic, non-linear, spatially inhomogeneous forcing. Well-posedness and L1-contraction is obtained in the class of entropy solutions. Our scope allows for porous medium operators Δ(|u|m−1u) for all m∈(1,∞), and Hölder continuous diffusion nonlinearity with exponent 1/2."}],"oa_version":"Preprint","volume":266,"issue":"6","publication_status":"published","language":[{"iso":"eng"}],"external_id":{"arxiv":["1803.06953"],"isi":["000456332500026"]},"article_processing_charge":"No","publist_id":"7989","author":[{"full_name":"Dareiotis, Konstantinos","last_name":"Dareiotis","first_name":"Konstantinos"},{"first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87","last_name":"Gerencser","full_name":"Gerencser, Mate"},{"full_name":"Gess, Benjamin","last_name":"Gess","first_name":"Benjamin"}],"title":"Entropy solutions for stochastic porous media equations","citation":{"mla":"Dareiotis, Konstantinos, et al. “Entropy Solutions for Stochastic Porous Media Equations.” Journal of Differential Equations, vol. 266, no. 6, Elsevier, 2019, pp. 3732–63, doi:10.1016/j.jde.2018.09.012.","ieee":"K. Dareiotis, M. Gerencser, and B. Gess, “Entropy solutions for stochastic porous media equations,” Journal of Differential Equations, vol. 266, no. 6. Elsevier, pp. 3732–3763, 2019.","short":"K. Dareiotis, M. Gerencser, B. Gess, Journal of Differential Equations 266 (2019) 3732–3763.","ama":"Dareiotis K, Gerencser M, Gess B. Entropy solutions for stochastic porous media equations. Journal of Differential Equations. 2019;266(6):3732-3763. doi:10.1016/j.jde.2018.09.012","apa":"Dareiotis, K., Gerencser, M., & Gess, B. (2019). Entropy solutions for stochastic porous media equations. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2018.09.012","chicago":"Dareiotis, Konstantinos, Mate Gerencser, and Benjamin Gess. “Entropy Solutions for Stochastic Porous Media Equations.” Journal of Differential Equations. Elsevier, 2019. https://doi.org/10.1016/j.jde.2018.09.012.","ista":"Dareiotis K, Gerencser M, Gess B. 2019. Entropy solutions for stochastic porous media equations. Journal of Differential Equations. 266(6), 3732–3763."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"quality_controlled":"1","publisher":"Elsevier","page":"3732-3763","date_created":"2018-12-11T11:44:26Z","date_published":"2019-03-05T00:00:00Z","doi":"10.1016/j.jde.2018.09.012","year":"2019","isi":1,"publication":"Journal of Differential Equations","day":"5"},{"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000463613800001"]},"publist_id":"7546","author":[{"full_name":"Gerencser, Mate","last_name":"Gerencser","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87","first_name":"Mate"},{"first_name":"Martin","last_name":"Hairer","full_name":"Hairer, Martin"}],"title":"Singular SPDEs in domains with boundaries","citation":{"ista":"Gerencser M, Hairer M. 2019. Singular SPDEs in domains with boundaries. Probability Theory and Related Fields. 173(3–4), 697–758.","chicago":"Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.” Probability Theory and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0841-1.","ieee":"M. Gerencser and M. Hairer, “Singular SPDEs in domains with boundaries,” Probability Theory and Related Fields, vol. 173, no. 3–4. Springer, pp. 697–758, 2019.","short":"M. Gerencser, M. Hairer, Probability Theory and Related Fields 173 (2019) 697–758.","ama":"Gerencser M, Hairer M. Singular SPDEs in domains with boundaries. Probability Theory and Related Fields. 2019;173(3-4):697–758. doi:10.1007/s00440-018-0841-1","apa":"Gerencser, M., & Hairer, M. (2019). Singular SPDEs in domains with boundaries. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-018-0841-1","mla":"Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.” Probability Theory and Related Fields, vol. 173, no. 3–4, Springer, 2019, pp. 697–758, doi:10.1007/s00440-018-0841-1."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"quality_controlled":"1","publisher":"Springer","acknowledgement":"MG thanks the support of the LMS Postdoctoral Mobility Grant.\r\n\r\n","page":"697–758","date_created":"2018-12-11T11:45:48Z","date_published":"2019-04-01T00:00:00Z","doi":"10.1007/s00440-018-0841-1","year":"2019","has_accepted_license":"1","isi":1,"publication":"Probability Theory and Related Fields","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)"},"type":"journal_article","article_type":"original","status":"public","_id":"319","file_date_updated":"2020-07-14T12:46:03Z","department":[{"_id":"JaMa"}],"date_updated":"2023-08-24T14:38:32Z","ddc":["510"],"scopus_import":"1","intvolume":" 173","month":"04","abstract":[{"text":"We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with boundary conditions. The calculus of modelled distributions established in Hairer (Invent Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4) is extended to this setting. We formulate and solve fixed point problems in these spaces with a class of kernels that is sufficiently large to cover in particular the Dirichlet and Neumann heat kernels. These results are then used to provide solution theories for the KPZ equation with Dirichlet and Neumann boundary conditions and for the 2D generalised parabolic Anderson model with Dirichlet boundary conditions. In the case of the KPZ equation with Neumann boundary conditions, we show that, depending on the class of mollifiers one considers, a “boundary renormalisation” takes place. In other words, there are situations in which a certain boundary condition is applied to an approximation to the KPZ equation, but the limiting process is the Hopf–Cole solution to the KPZ equation with a different boundary condition.","lang":"eng"}],"oa_version":"Published Version","volume":173,"issue":"3-4","publication_status":"published","publication_identifier":{"eissn":["14322064"],"issn":["01788051"]},"language":[{"iso":"eng"}],"file":[{"creator":"dernst","date_updated":"2020-07-14T12:46:03Z","file_size":893182,"date_created":"2018-12-17T16:25:24Z","file_name":"2018_ProbTheory_Gerencser.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"5722","checksum":"288d16ef7291242f485a9660979486e3"}]},{"_id":"6028","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)"},"type":"journal_article","status":"public","date_updated":"2023-08-24T14:44:31Z","ddc":["500"],"file_date_updated":"2020-07-14T12:47:17Z","department":[{"_id":"JaMa"}],"abstract":[{"text":"We give a construction allowing us to build local renormalized solutions to general quasilinear stochastic PDEs within the theory of regularity structures, thus greatly generalizing the recent results of [1, 5, 11]. Loosely speaking, our construction covers quasilinear variants of all classes of equations for which the general construction of [3, 4, 7] applies, including in particular one‐dimensional systems with KPZ‐type nonlinearities driven by space‐time white noise. In a less singular and more specific case, we furthermore show that the counterterms introduced by the renormalization procedure are given by local functionals of the solution. The main feature of our construction is that it allows exploitation of a number of existing results developed for the semilinear case, so that the number of additional arguments it requires is relatively small.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 72","month":"02","publication_status":"published","language":[{"iso":"eng"}],"file":[{"file_id":"7237","checksum":"09aec427eb48c0f96a1cce9ff53f013b","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2020-01-07T13:25:55Z","file_name":"2019_Wiley_Gerencser.pdf","date_updated":"2020-07-14T12:47:17Z","file_size":381350,"creator":"kschuh"}],"volume":72,"issue":"9","citation":{"ista":"Gerencser M, Hairer M. 2019. A solution theory for quasilinear singular SPDEs. Communications on Pure and Applied Mathematics. 72(9), 1983–2005.","chicago":"Gerencser, Mate, and Martin Hairer. “A Solution Theory for Quasilinear Singular SPDEs.” Communications on Pure and Applied Mathematics. Wiley, 2019. https://doi.org/10.1002/cpa.21816.","short":"M. Gerencser, M. Hairer, Communications on Pure and Applied Mathematics 72 (2019) 1983–2005.","ieee":"M. Gerencser and M. Hairer, “A solution theory for quasilinear singular SPDEs,” Communications on Pure and Applied Mathematics, vol. 72, no. 9. Wiley, pp. 1983–2005, 2019.","apa":"Gerencser, M., & Hairer, M. (2019). A solution theory for quasilinear singular SPDEs. Communications on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.21816","ama":"Gerencser M, Hairer M. A solution theory for quasilinear singular SPDEs. 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