--- _id: '10145' abstract: - lang: eng text: We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique. 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. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 citation: ama: Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 2023;58:573-615. doi:10.1007/s11118-021-09951-y apa: Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-021-09951-y chicago: Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis. Springer Nature, 2023. https://doi.org/10.1007/s11118-021-09951-y. ieee: L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals and applications,” Potential Analysis, vol. 58. Springer Nature, pp. 573–615, 2023. ista: Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 58, 573–615. mla: Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis, vol. 58, Springer Nature, 2023, pp. 573–615, doi:10.1007/s11118-021-09951-y. short: L. Dello Schiavo, Potential Analysis 58 (2023) 573–615. date_created: 2021-10-17T22:01:17Z date_published: 2023-03-01T00:00:00Z date_updated: 2023-10-04T09:19:12Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s11118-021-09951-y ec_funded: 1 external_id: arxiv: - '2003.01366' isi: - '000704213400001' file: - access_level: open_access checksum: 625526482be300ca7281c91c30d41725 content_type: application/pdf creator: dernst date_created: 2023-10-04T09:18:59Z date_updated: 2023-10-04T09:18:59Z file_id: '14387' file_name: 2023_PotentialAnalysis_DelloSchiavo.pdf file_size: 806391 relation: main_file success: 1 file_date_updated: 2023-10-04T09:18:59Z has_accepted_license: '1' intvolume: ' 58' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 573-615 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Potential Analysis publication_identifier: eissn: - 1572-929X issn: - 0926-2601 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Ergodic decomposition of Dirichlet forms via direct integrals and applications tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 58 year: '2023' ... --- _id: '12087' abstract: - lang: eng text: Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups. 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). article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 - first_name: Haonan full_name: Zhang, Haonan id: D8F41E38-9E66-11E9-A9E2-65C2E5697425 last_name: Zhang citation: ama: Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 2023;24:717-750. doi:10.1007/s00023-022-01220-x apa: Wirth, M., & Zhang, H. (2023). Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-022-01220-x 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. 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. ista: Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 24, 717–750. mla: Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” Annales Henri Poincare, vol. 24, Springer Nature, 2023, pp. 717–50, doi:10.1007/s00023-022-01220-x. short: M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750. date_created: 2022-09-11T22:01:57Z date_published: 2023-03-01T00:00:00Z date_updated: 2023-08-14T11:39:28Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s00023-022-01220-x ec_funded: 1 external_id: arxiv: - '2105.08303' isi: - '000837499800002' file: - access_level: open_access checksum: 8c7b185eba5ccd92ef55c120f654222c content_type: application/pdf creator: dernst date_created: 2023-08-14T11:38:28Z date_updated: 2023-08-14T11:38:28Z file_id: '14051' file_name: 2023_AnnalesHenriPoincare_Wirth.pdf file_size: 554871 relation: main_file success: 1 file_date_updated: 2023-08-14T11:38:28Z has_accepted_license: '1' intvolume: ' 24' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 717-750 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6 grant_number: M03337 name: Curvature-dimension in noncommutative analysis - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 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 publication: Annales Henri Poincare publication_identifier: issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Curvature-dimension conditions for symmetric quantum Markov semigroups tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2023' ... --- _id: '12104' 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. 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). article_number: '9' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 citation: 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 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. 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. ista: Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9. mla: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations, vol. 23, no. 1, 9, Springer Nature, 2023, doi:10.1007/s00028-022-00859-7. short: L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023). date_created: 2023-01-08T23:00:53Z date_published: 2023-01-01T00:00:00Z date_updated: 2023-06-28T11:54:35Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s00028-022-00859-7 ec_funded: 1 external_id: isi: - '000906214600004' file: - access_level: open_access checksum: 1f34f3e2cb521033de6154f274ea3a4e content_type: application/pdf creator: dernst date_created: 2023-01-20T10:45:06Z date_updated: 2023-01-20T10:45:06Z file_id: '12325' file_name: 2023_JourEvolutionEquations_DelloSchiavo.pdf file_size: 422612 relation: main_file success: 1 file_date_updated: 2023-01-20T10:45:06Z has_accepted_license: '1' intvolume: ' 23' isi: 1 issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c grant_number: E208 name: Configuration Spaces over Non-Smooth Spaces - _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833 grant_number: ESP156_N name: Gradient flow techniques for quantum Markov semigroups publication: Journal of Evolution Equations publication_identifier: eissn: - 1424-3202 issn: - 1424-3199 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Ergodic decompositions of Dirichlet forms under order isomorphisms tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 23 year: '2023' ... --- _id: '12521' abstract: - lang: eng text: Differentiated X chromosomes are expected to have higher rates of adaptive divergence than autosomes, if new beneficial mutations are recessive (the “faster-X effect”), largely because these mutations are immediately exposed to selection in males. The evolution of X chromosomes after they stop recombining in males, but before they become hemizygous, has not been well explored theoretically. We use the diffusion approximation to infer substitution rates of beneficial and deleterious mutations under such a scenario. Our results show that selection is less efficient on diploid X loci than on autosomal and hemizygous X loci under a wide range of parameters. This “slower-X” effect is stronger for genes affecting primarily (or only) male fitness, and for sexually antagonistic genes. These unusual dynamics suggest that some of the peculiar features of X chromosomes, such as the differential accumulation of genes with sex-specific functions, may start arising earlier than previously appreciated. acknowledgement: We thank the Vicoso and Barton groups and ISTA Scientific Computing Unit. We also thank two anonymous reviewers for their valuable comments. This work was supported by the European Research Council under the European Union’s Horizon 2020 research and innovation program (grant agreements no. 715257 and no. 716117). article_number: qrac004 article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Andrea full_name: Mrnjavac, Andrea id: 353FAC84-AE61-11E9-8BFC-00D3E5697425 last_name: Mrnjavac - first_name: Kseniia full_name: Khudiakova, Kseniia id: 4E6DC800-AE37-11E9-AC72-31CAE5697425 last_name: Khudiakova orcid: 0000-0002-6246-1465 - first_name: Nicholas H full_name: Barton, Nicholas H id: 4880FE40-F248-11E8-B48F-1D18A9856A87 last_name: Barton orcid: 0000-0002-8548-5240 - first_name: Beatriz full_name: Vicoso, Beatriz id: 49E1C5C6-F248-11E8-B48F-1D18A9856A87 last_name: Vicoso orcid: 0000-0002-4579-8306 citation: ama: 'Mrnjavac A, Khudiakova K, Barton NH, Vicoso B. Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution. Evolution Letters. 2023;7(1). doi:10.1093/evlett/qrac004' apa: 'Mrnjavac, A., Khudiakova, K., Barton, N. H., & Vicoso, B. (2023). Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution. Evolution Letters. Oxford University Press. https://doi.org/10.1093/evlett/qrac004' chicago: 'Mrnjavac, Andrea, Kseniia Khudiakova, Nicholas H Barton, and Beatriz Vicoso. “Slower-X: Reduced Efficiency of Selection in the Early Stages of X Chromosome Evolution.” Evolution Letters. Oxford University Press, 2023. https://doi.org/10.1093/evlett/qrac004.' ieee: 'A. Mrnjavac, K. Khudiakova, N. H. Barton, and B. Vicoso, “Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution,” Evolution Letters, vol. 7, no. 1. Oxford University Press, 2023.' ista: 'Mrnjavac A, Khudiakova K, Barton NH, Vicoso B. 2023. Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution. Evolution Letters. 7(1), qrac004.' mla: 'Mrnjavac, Andrea, et al. “Slower-X: Reduced Efficiency of Selection in the Early Stages of X Chromosome Evolution.” Evolution Letters, vol. 7, no. 1, qrac004, Oxford University Press, 2023, doi:10.1093/evlett/qrac004.' short: A. Mrnjavac, K. Khudiakova, N.H. Barton, B. Vicoso, Evolution Letters 7 (2023). date_created: 2023-02-06T13:59:12Z date_published: 2023-02-01T00:00:00Z date_updated: 2023-08-16T11:44:32Z day: '01' ddc: - '570' department: - _id: GradSch - _id: BeVi doi: 10.1093/evlett/qrac004 ec_funded: 1 external_id: isi: - '001021692200001' pmid: - '37065438' file: - access_level: open_access checksum: a240a041cb9b9b7c8ba93a4706674a3f content_type: application/pdf creator: dernst date_created: 2023-08-16T11:43:33Z date_updated: 2023-08-16T11:43:33Z file_id: '14068' file_name: 2023_EvLetters_Mrnjavac.pdf file_size: 2592189 relation: main_file success: 1 file_date_updated: 2023-08-16T11:43:33Z has_accepted_license: '1' intvolume: ' 7' isi: 1 issue: '1' keyword: - Genetics - Ecology - Evolution - Behavior and Systematics language: - iso: eng month: '02' oa: 1 oa_version: Published Version pmid: 1 project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 250BDE62-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '715257' name: Prevalence and Influence of Sexual Antagonism on Genome Evolution publication: Evolution Letters publication_identifier: issn: - 2056-3744 publication_status: published publisher: Oxford University Press quality_controlled: '1' scopus_import: '1' status: public title: 'Slower-X: Reduced efficiency of selection in the early stages of X chromosome evolution' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 7 year: '2023' ... --- _id: '12911' 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.' 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." article_number: '109963' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Augusto full_name: Gerolin, Augusto last_name: Gerolin - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: 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 chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.109963. ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” Journal of Functional Analysis, vol. 285, no. 4. Elsevier, 2023. 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. 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. short: D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023). date_created: 2023-05-07T22:01:02Z date_published: 2023-08-15T00:00:00Z date_updated: 2023-11-14T13:21:01Z day: '15' department: - _id: RoSe - _id: JaMa doi: 10.1016/j.jfa.2023.109963 ec_funded: 1 external_id: arxiv: - '2106.11217' isi: - '000990804300001' intvolume: ' 285' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2106.11217 month: '08' oa: 1 oa_version: Preprint project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 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 - _id: 260482E2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: ' F06504' name: Taming Complexity in Partial Di erential Systems publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '9792' relation: earlier_version status: public scopus_import: '1' status: public title: A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 285 year: '2023' ... --- _id: '12959' 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." 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). article_number: '143' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Peter full_name: Gladbach, Peter last_name: Gladbach - first_name: Eva full_name: Kopfer, Eva last_name: Kopfer - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: 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 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 chicago: Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” Calculus of Variations and Partial Differential Equations. Springer Nature, 2023. https://doi.org/10.1007/s00526-023-02472-z. ieee: P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of dynamical optimal transport on periodic graphs,” Calculus of Variations and Partial Differential Equations, vol. 62, no. 5. Springer Nature, 2023. 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. short: P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and Partial Differential Equations 62 (2023). date_created: 2023-05-14T22:01:00Z date_published: 2023-04-28T00:00:00Z date_updated: 2023-10-04T11:34:49Z day: '28' ddc: - '510' department: - _id: JaMa doi: 10.1007/s00526-023-02472-z ec_funded: 1 external_id: arxiv: - '2110.15321' isi: - '000980588900001' file: - access_level: open_access checksum: 359bee38d94b7e0aa73925063cb8884d content_type: application/pdf creator: dernst date_created: 2023-10-04T11:34:10Z date_updated: 2023-10-04T11:34:10Z file_id: '14393' file_name: 2023_CalculusEquations_Gladbach.pdf file_size: 1240995 relation: main_file success: 1 file_date_updated: 2023-10-04T11:34:10Z has_accepted_license: '1' intvolume: ' 62' isi: 1 issue: '5' language: - iso: eng month: '04' oa: 1 oa_version: Published Version 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 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 260788DE-B435-11E9-9278-68D0E5697425 call_identifier: FWF name: Dissipation and Dispersion in Nonlinear Partial Differential Equations publication: Calculus of Variations and Partial Differential Equations publication_identifier: eissn: - 1432-0835 issn: - 0944-2669 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Homogenisation of dynamical optimal transport on periodic graphs tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 62 year: '2023' ... --- _id: '11330' 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. 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)." article_number: '19' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 citation: 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 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 chicago: Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02911-9. ieee: M. Wirth, “A dual formula for the noncommutative transport distance,” Journal of Statistical Physics, vol. 187, no. 2. Springer Nature, 2022. ista: Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19. 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. short: M. Wirth, Journal of Statistical Physics 187 (2022). date_created: 2022-04-24T22:01:43Z date_published: 2022-04-08T00:00:00Z date_updated: 2023-08-03T06:37:49Z day: '08' ddc: - '510' - '530' department: - _id: JaMa doi: 10.1007/s10955-022-02911-9 ec_funded: 1 external_id: isi: - '000780305000001' file: - access_level: open_access checksum: f3e0b00884b7dde31347a3756788b473 content_type: application/pdf creator: dernst date_created: 2022-04-29T11:24:23Z date_updated: 2022-04-29T11:24:23Z file_id: '11338' file_name: 2022_JourStatisticalPhysics_Wirth.pdf file_size: 362119 relation: main_file success: 1 file_date_updated: 2022-04-29T11:24:23Z has_accepted_license: '1' intvolume: ' 187' isi: 1 issue: '2' language: - iso: eng month: '04' oa: 1 oa_version: Published Version project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Journal of Statistical Physics publication_identifier: eissn: - '15729613' issn: - '00224715' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A dual formula for the noncommutative transport distance tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 187 year: '2022' ... --- _id: '11354' abstract: - lang: eng text: We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics. acknowledgement: Research supported by the Sonderforschungsbereich 1060 and the Hausdorff Center for Mathematics. The author gratefully acknowledges funding of his current position at IST Austria by the Austrian Science Fund (FWF) grant F65 and by the European Research Council (ERC, Grant agreement No. 716117, awarded to Prof. Dr. Jan Maas). article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 citation: 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 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. 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. 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. date_created: 2022-05-08T22:01:44Z date_published: 2022-03-01T00:00:00Z date_updated: 2023-10-17T12:50:24Z day: '01' department: - _id: JaMa doi: 10.1214/21-AOP1541 ec_funded: 1 external_id: arxiv: - '1811.11598' isi: - '000773518500005' intvolume: ' 50' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.1811.11598' month: '03' oa: 1 oa_version: Preprint page: 591-648 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 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: Annals of Probability publication_identifier: eissn: - 2168-894X issn: - 0091-1798 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 50 year: '2022' ... --- _id: '11700' 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. 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." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Matthias full_name: Erbar, Matthias last_name: Erbar - first_name: Dominik L full_name: Forkert, Dominik L id: 35C79D68-F248-11E8-B48F-1D18A9856A87 last_name: Forkert - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Delio full_name: Mugnolo, Delio last_name: Mugnolo citation: 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 chicago: Erbar, Matthias, Dominik L Forkert, Jan Maas, and Delio Mugnolo. “Gradient Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric Graph.” Networks and Heterogeneous Media. American Institute of Mathematical Sciences, 2022. https://doi.org/10.3934/nhm.2022023. ieee: M. Erbar, D. L. Forkert, J. Maas, and D. Mugnolo, “Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph,” Networks and Heterogeneous Media, vol. 17, no. 5. American Institute of Mathematical Sciences, pp. 687–717, 2022. 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. date_created: 2022-07-31T22:01:46Z date_published: 2022-10-01T00:00:00Z date_updated: 2023-08-03T12:25:49Z day: '01' department: - _id: JaMa doi: 10.3934/nhm.2022023 ec_funded: 1 external_id: arxiv: - '2105.05677' isi: - '000812422100001' intvolume: ' 17' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2105.05677 month: '10' oa: 1 oa_version: Preprint page: 687-717 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 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: Networks and Heterogeneous Media publication_identifier: eissn: - 1556-181X issn: - 1556-1801 publication_status: published publisher: American Institute of Mathematical Sciences quality_controlled: '1' scopus_import: '1' status: public title: Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 17 year: '2022' ... --- _id: '11739' 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. acknowledgement: This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme grant 716117 and by the AustrianScience Fund (FWF) through grants F65 and W1245. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Dominik L full_name: Forkert, Dominik L id: 35C79D68-F248-11E8-B48F-1D18A9856A87 last_name: Forkert - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: 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 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 chicago: Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21M1410968. ieee: D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” SIAM Journal on Mathematical Analysis, vol. 54, no. 4. Society for Industrial and Applied Mathematics, pp. 4297–4333, 2022. 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. 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. short: D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis 54 (2022) 4297–4333. date_created: 2022-08-07T22:01:59Z date_published: 2022-07-18T00:00:00Z date_updated: 2023-08-03T12:37:21Z day: '18' department: - _id: JaMa doi: 10.1137/21M1410968 ec_funded: 1 external_id: arxiv: - '2008.10962' isi: - '000889274600001' intvolume: ' 54' isi: 1 issue: '4' keyword: - Fokker--Planck equation - gradient flow - evolutionary $\Gamma$-convergence language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2008.10962' month: '07' oa: 1 oa_version: Preprint page: 4297-4333 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 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 260788DE-B435-11E9-9278-68D0E5697425 call_identifier: FWF name: Dissipation and Dispersion in Nonlinear Partial Differential Equations publication: SIAM Journal on Mathematical Analysis publication_identifier: eissn: - 1095-7154 issn: - 0036-1410 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' related_material: record: - id: '10022' relation: earlier_version status: public scopus_import: '1' status: public title: Evolutionary $\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 54 year: '2022' ... --- _id: '10588' abstract: - lang: eng text: We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds. 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." article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 - first_name: Kohei full_name: Suzuki, Kohei last_name: Suzuki citation: 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 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. 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. 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. short: L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832. date_created: 2022-01-02T23:01:35Z date_published: 2022-12-01T00:00:00Z date_updated: 2023-08-02T13:39:05Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s00208-021-02331-2 ec_funded: 1 external_id: arxiv: - '2110.05137' isi: - '000734150200001' file: - access_level: open_access checksum: 2593abbf195e38efa93b6006b1e90eb1 content_type: application/pdf creator: alisjak date_created: 2022-01-03T11:08:31Z date_updated: 2022-01-03T11:08:31Z file_id: '10596' file_name: 2021_MathAnn_DelloSchiavo.pdf file_size: 410090 relation: main_file success: 1 file_date_updated: 2022-01-03T11:08:31Z has_accepted_license: '1' intvolume: ' 384' isi: 1 keyword: - quasi curvature-dimension condition - sub-riemannian geometry - Sobolev-to-Lipschitz property - Varadhan short-time asymptotics language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 1815-1832 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 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Mathematische Annalen publication_identifier: eissn: - 1432-1807 issn: - 0025-5831 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Sobolev-to-Lipschitz property on QCD- spaces and applications tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 384 year: '2022' ... --- _id: '12177' 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. 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." article_processing_charge: No article_type: original author: - first_name: Tommaso full_name: Cremaschi, Tommaso last_name: Cremaschi - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 citation: 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 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 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. 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. ista: Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 9(43), 445–459. mla: Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” Proceedings of the American Mathematical Society, Series B, vol. 9, no. 43, American Mathematical Society, 2022, pp. 445–59, doi:10.1090/bproc/134. short: T. Cremaschi, L. Dello Schiavo, Proceedings of the American Mathematical Society, Series B 9 (2022) 445–459. date_created: 2023-01-12T12:12:17Z date_published: 2022-11-02T00:00:00Z date_updated: 2023-01-26T13:04:13Z day: '02' ddc: - '510' department: - _id: JaMa doi: 10.1090/bproc/134 ec_funded: 1 file: - access_level: open_access checksum: cb4a79937c1f60d4c329a10ee797f0d2 content_type: application/pdf creator: dernst date_created: 2023-01-26T13:02:07Z date_updated: 2023-01-26T13:02:07Z file_id: '12404' file_name: 2022_ProceedingsAMS_Cremaschi.pdf file_size: 326471 relation: main_file success: 1 file_date_updated: 2023-01-26T13:02:07Z has_accepted_license: '1' intvolume: ' 9' issue: '43' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 445-459 project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Proceedings of the American Mathematical Society, Series B publication_identifier: issn: - 2330-1511 publication_status: published publisher: American Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: Effective contraction of Skinning maps tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 9 year: '2022' ... --- _id: '10023' 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. acknowledgement: I.K. acknowledges support from the U.S. National Science Foundation under Grant NSF-DMS-20-04997. J.M. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117) and from the Austrian Science Fund (FWF) through project F65. W.S. acknowledges support from the Austrian Science Fund (FWF) under grant P28861 and by the Vienna Science and Technology Fund (WWTF) through projects MA14-008 and MA16-021. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Ioannis full_name: Karatzas, Ioannis last_name: Karatzas - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Walter full_name: Schachermayer, Walter last_name: Schachermayer citation: 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 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 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. 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. 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. short: I. Karatzas, J. Maas, W. Schachermayer, Communications in Information and Systems 21 (2021) 481–536. date_created: 2021-09-19T08:53:19Z date_published: 2021-06-04T00:00:00Z date_updated: 2021-09-20T12:51:18Z day: '04' department: - _id: JaMa doi: 10.4310/CIS.2021.v21.n4.a1 ec_funded: 1 external_id: arxiv: - '2005.14177' intvolume: ' 21' issue: '4' keyword: - Markov Chain - relative entropy - time reversal - steepest descent - gradient flow language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2005.14177 month: '06' oa: 1 oa_version: Preprint page: 481-536 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 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: Communications in Information and Systems publication_identifier: issn: - 1526-7555 publication_status: published publisher: International Press quality_controlled: '1' status: public title: Trajectorial dissipation and gradient flow for the relative entropy in Markov chains type: journal_article user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 21 year: '2021' ... --- _id: '10070' 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. 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.' article_number: '109234' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 - first_name: Kohei full_name: Suzuki, Kohei last_name: Suzuki citation: 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 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 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. 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. ista: Dello Schiavo L, Suzuki K. 2021. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. 281(11), 109234. mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” Journal of Functional Analysis, vol. 281, no. 11, 109234, Elsevier, 2021, doi:10.1016/j.jfa.2021.109234. short: L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021). date_created: 2021-10-03T22:01:21Z date_published: 2021-09-15T00:00:00Z date_updated: 2023-08-14T07:05:44Z day: '15' department: - _id: JaMa doi: 10.1016/j.jfa.2021.109234 ec_funded: 1 external_id: arxiv: - '2008.01492' isi: - '000703896600005' intvolume: ' 281' isi: 1 issue: '11' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2008.01492 month: '09' oa: 1 oa_version: Preprint project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 281 year: '2021' ... --- _id: '9733' abstract: - lang: eng text: This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 citation: 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 chicago: Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:9733. ieee: D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and Technology Austria, 2021. 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. short: D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and Technology Austria, 2021. date_created: 2021-07-27T15:48:30Z date_published: 2021-08-20T00:00:00Z date_updated: 2024-03-06T12:30:44Z day: '20' ddc: - '515' - '519' - '539' degree_awarded: PhD department: - _id: GradSch - _id: RoSe - _id: JaMa doi: 10.15479/at:ista:9733 ec_funded: 1 file: - access_level: open_access checksum: e88bb8ca43948abe060eb2d2fa719881 content_type: application/pdf creator: dfelicia date_created: 2021-08-19T14:03:48Z date_updated: 2021-09-06T09:28:56Z file_id: '9944' file_name: Thesis_FeliciangeliA.pdf file_size: 1958710 relation: main_file - access_level: closed checksum: 72810843abee83705853505b3f8348aa content_type: application/octet-stream creator: dfelicia date_created: 2021-08-19T14:06:35Z date_updated: 2022-03-10T12:13:57Z file_id: '9945' file_name: thesis.7z file_size: 3771669 relation: source_file file_date_updated: 2022-03-10T12:13:57Z has_accepted_license: '1' language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: '180' project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 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 - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '9787' relation: part_of_dissertation status: public - id: '9792' relation: part_of_dissertation status: public - id: '9225' relation: part_of_dissertation status: public - id: '9781' relation: part_of_dissertation status: public - id: '9791' relation: part_of_dissertation status: public status: public supervisor: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 title: The polaron at strong coupling tmp: image: /image/cc_by_nd.png legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0) short: CC BY-ND (4.0) type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2021' ... --- _id: '9792' 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.' 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].' article_number: '2106.11217' article_processing_charge: No arxiv: 1 author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Augusto full_name: Gerolin, Augusto last_name: Gerolin - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: 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 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. ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” arXiv. . 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. short: D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.). date_created: 2021-08-06T09:07:12Z date_published: 2021-07-21T00:00:00Z date_updated: 2023-11-14T13:21:01Z day: '21' ddc: - '510' department: - _id: RoSe - _id: JaMa doi: 10.48550/arXiv.2106.11217 ec_funded: 1 external_id: arxiv: - '2106.11217' has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2106.11217 month: '07' oa: 1 oa_version: Preprint project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 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 publication: arXiv publication_status: submitted related_material: record: - id: '9733' relation: dissertation_contains status: public - id: '10030' relation: dissertation_contains status: public - id: '12911' relation: later_version status: public status: public title: A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '8758' abstract: - lang: eng 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. 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). article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Alexander full_name: Mielke, Alexander last_name: Mielke citation: 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 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 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. 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. 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. 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. short: J. Maas, A. Mielke, Journal of Statistical Physics 181 (2020) 2257–2303. date_created: 2020-11-15T23:01:18Z date_published: 2020-12-01T00:00:00Z date_updated: 2023-08-22T13:24:27Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s10955-020-02663-4 ec_funded: 1 external_id: arxiv: - '2004.02831' isi: - '000587107200002' file: - access_level: open_access checksum: bc2b63a90197b97cbc73eccada4639f5 content_type: application/pdf creator: dernst date_created: 2021-02-04T10:29:11Z date_updated: 2021-02-04T10:29:11Z file_id: '9087' file_name: 2020_JourStatPhysics_Maas.pdf file_size: 753596 relation: main_file success: 1 file_date_updated: 2021-02-04T10:29:11Z has_accepted_license: '1' intvolume: ' 181' isi: 1 issue: '6' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 2257-2303 project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 260482E2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: ' F06504' name: Taming Complexity in Partial Di erential Systems publication: Journal of Statistical Physics publication_identifier: eissn: - '15729613' issn: - '00224715' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Modeling of chemical reaction systems with detailed balance using gradient structures tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 181 year: '2020' ... --- _id: '74' abstract: - lang: eng text: "We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean space, motivated by the famous theorem of Gromov about \ the waist of radially symmetric Gaussian measures. In particular, it turns our possible to extend Gromov’s original result to the case of not necessarily \ radially symmetric Gaussian measure. We also provide examples of measures having no t-neighborhood waist property, including a rather wide class\r\nof compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument \ to produce some estimates of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures." article_processing_charge: No arxiv: 1 author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Roman full_name: Karasev, Roman last_name: Karasev citation: 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 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. 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. 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. date_created: 2018-12-11T11:44:29Z date_published: 2020-06-21T00:00:00Z date_updated: 2023-08-17T13:48:31Z day: '21' department: - _id: HeEd - _id: JaMa doi: 10.1007/978-3-030-36020-7_1 ec_funded: 1 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' intvolume: ' 2256' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1808.07350 month: '06' oa: 1 oa_version: Preprint page: 1-27 project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Geometric Aspects of Functional Analysis publication_identifier: eisbn: - '9783030360207' eissn: - '16179692' isbn: - '9783030360191' issn: - '00758434' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' series_title: LNM status: public title: Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures type: book_chapter user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 2256 year: '2020' ... --- _id: '7573' abstract: - lang: eng text: This paper deals with dynamical optimal transport metrics defined by spatial discretisation of the Benamou–Benamou formula for the Kantorovich metric . Such metrics appear naturally in discretisations of -gradient flow formulations for dissipative PDE. However, it has recently been shown that these metrics do not in general converge to , unless strong geometric constraints are imposed on the discrete mesh. In this paper we prove that, in a 1-dimensional periodic setting, discrete transport metrics converge to a limiting transport metric with a non-trivial effective mobility. This mobility depends sensitively on the geometry of the mesh and on the non-local mobility at the discrete level. Our result quantifies to what extent discrete transport can make use of microstructure in the mesh to reduce the cost of transport. 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. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Peter full_name: Gladbach, Peter last_name: Gladbach - first_name: Eva full_name: Kopfer, Eva last_name: Kopfer - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: 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 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 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. 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. 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. short: P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Journal de Mathematiques Pures et Appliquees 139 (2020) 204–234. date_created: 2020-03-08T23:00:47Z date_published: 2020-07-01T00:00:00Z date_updated: 2023-09-07T13:31:05Z day: '01' department: - _id: JaMa doi: 10.1016/j.matpur.2020.02.008 ec_funded: 1 external_id: arxiv: - '1905.05757' isi: - '000539439400008' intvolume: ' 139' isi: 1 issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1905.05757 month: '07' oa: 1 oa_version: Preprint page: 204-234 project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 260482E2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: ' F06504' name: Taming Complexity in Partial Di erential Systems - _id: 260788DE-B435-11E9-9278-68D0E5697425 call_identifier: FWF name: Dissipation and Dispersion in Nonlinear Partial Differential Equations publication: Journal de Mathematiques Pures et Appliquees publication_identifier: issn: - '00217824' publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '10030' relation: dissertation_contains status: public scopus_import: '1' status: public title: Homogenisation of one-dimensional discrete optimal transport type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 139 year: '2020' ... --- _id: '7629' 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." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Dominik L full_name: Forkert, Dominik L id: 35C79D68-F248-11E8-B48F-1D18A9856A87 last_name: Forkert citation: 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 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 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. 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. 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. 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. 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. date_created: 2020-04-02T06:40:23Z date_published: 2020-03-31T00:00:00Z date_updated: 2023-09-07T13:03:12Z day: '31' ddc: - '510' degree_awarded: PhD department: - _id: JaMa doi: 10.15479/AT:ISTA:7629 ec_funded: 1 file: - access_level: open_access checksum: c814a1a6195269ca6fe48b0dca45ae8a content_type: application/pdf creator: dernst date_created: 2020-04-14T10:47:59Z date_updated: 2020-07-14T12:48:01Z file_id: '7657' file_name: Thesis_Forkert_PDFA.pdf file_size: 3297129 relation: main_file - access_level: closed checksum: ceafb53f923d1b5bdf14b2b0f22e4a81 content_type: application/x-zip-compressed creator: dernst date_created: 2020-04-14T10:47:59Z date_updated: 2020-07-14T12:48:01Z file_id: '7658' file_name: Thesis_Forkert_source.zip file_size: 1063908 relation: source_file file_date_updated: 2020-07-14T12:48:01Z has_accepted_license: '1' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: '154' project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria status: public supervisor: - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 title: Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2020' ...