--- _id: '12216' abstract: - lang: eng text: Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments. acknowledgement: Work partially supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Eric A. full_name: Carlen, Eric A. last_name: Carlen - first_name: Haonan full_name: Zhang, Haonan id: D8F41E38-9E66-11E9-A9E2-65C2E5697425 last_name: Zhang citation: ama: Carlen EA, Zhang H. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 2022;654:289-310. doi:10.1016/j.laa.2022.09.001 apa: Carlen, E. A., & Zhang, H. (2022). Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2022.09.001 chicago: Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” Linear Algebra and Its Applications. Elsevier, 2022. https://doi.org/10.1016/j.laa.2022.09.001. ieee: E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem and related inequalities,” Linear Algebra and its Applications, vol. 654. Elsevier, pp. 289–310, 2022. ista: Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 654, 289–310. mla: Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” Linear Algebra and Its Applications, vol. 654, Elsevier, 2022, pp. 289–310, doi:10.1016/j.laa.2022.09.001. short: E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310. date_created: 2023-01-16T09:46:38Z date_published: 2022-12-01T00:00:00Z date_updated: 2023-08-04T09:24:51Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1016/j.laa.2022.09.001 external_id: isi: - '000860689600014' file: - access_level: open_access checksum: cf3cb7e7e34baa967849f01d8f0c1ae4 content_type: application/pdf creator: dernst date_created: 2023-01-27T08:08:39Z date_updated: 2023-01-27T08:08:39Z file_id: '12415' file_name: 2022_LinearAlgebra_Carlen.pdf file_size: 441184 relation: main_file success: 1 file_date_updated: 2023-01-27T08:08:39Z has_accepted_license: '1' intvolume: ' 654' isi: 1 keyword: - Discrete Mathematics and Combinatorics - Geometry and Topology - Numerical Analysis - Algebra and Number Theory language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 289-310 project: - _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6 grant_number: M03337 name: Curvature-dimension in noncommutative analysis publication: Linear Algebra and its Applications publication_identifier: issn: - 0024-3795 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Monotonicity versions of Epstein's concavity theorem and related inequalities 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: 654 year: '2022' ... --- _id: '12281' abstract: - lang: eng text: We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary conditions as hydrodynamic equation. In our approach, we combine duality and first-second class particle techniques to reduce the scaling limit of the inclusion process to the limiting behavior of a single, non-interacting, particle. acknowledgement: "C.F. and P.G. thank FCT/Portugal for support through the project UID/MAT/04459/2013.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative programme (grant agreement No. 715734). F.S. was founded by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.\r\nF.S. wishes to thank Joe P. Chen for some fruitful discussions at an early stage of this work. F.S. thanks CAMGSD, IST, Lisbon, where part of this work has been done, and the European research and innovative programme No. 715734 for the kind hospitality." article_processing_charge: No article_type: original author: - first_name: Chiara full_name: Franceschini, Chiara last_name: Franceschini - first_name: Patrícia full_name: Gonçalves, Patrícia last_name: Gonçalves - first_name: Federico full_name: Sau, Federico id: E1836206-9F16-11E9-8814-AEFDE5697425 last_name: Sau citation: ama: 'Franceschini C, Gonçalves P, Sau F. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 2022;28(2):1340-1381. doi:10.3150/21-bej1390' apa: 'Franceschini, C., Gonçalves, P., & Sau, F. (2022). Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. Bernoulli Society for Mathematical Statistics and Probability. https://doi.org/10.3150/21-bej1390' chicago: 'Franceschini, Chiara, Patrícia Gonçalves, and Federico Sau. “Symmetric Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” Bernoulli. Bernoulli Society for Mathematical Statistics and Probability, 2022. https://doi.org/10.3150/21-bej1390.' ieee: 'C. Franceschini, P. Gonçalves, and F. Sau, “Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics,” Bernoulli, vol. 28, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1340–1381, 2022.' ista: 'Franceschini C, Gonçalves P, Sau F. 2022. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 28(2), 1340–1381.' mla: 'Franceschini, Chiara, et al. “Symmetric Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” Bernoulli, vol. 28, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2022, pp. 1340–81, doi:10.3150/21-bej1390.' short: C. Franceschini, P. Gonçalves, F. Sau, Bernoulli 28 (2022) 1340–1381. date_created: 2023-01-16T10:03:04Z date_published: 2022-05-01T00:00:00Z date_updated: 2023-08-04T10:27:35Z day: '01' department: - _id: JaMa doi: 10.3150/21-bej1390 ec_funded: 1 external_id: arxiv: - '2007.11998' isi: - '000766619100025' intvolume: ' 28' isi: 1 issue: '2' keyword: - Statistics and Probability language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2007.11998 month: '05' oa: 1 oa_version: Preprint page: 1340-1381 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Bernoulli publication_identifier: issn: - 1350-7265 publication_status: published publisher: Bernoulli Society for Mathematical Statistics and Probability quality_controlled: '1' scopus_import: '1' status: public title: 'Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics' type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 28 year: '2022' ... --- _id: '10797' abstract: - lang: eng text: We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then we derive new orthogonal polynomial dualities. From the classical dualities, we derive the uniqueness of the non-equilibrium steady state and obtain correlation inequalities. Starting from the orthogonal polynomial dualities, we show universal properties of n-point correlation functions in the non-equilibrium steady state for systems with at most two different reservoir parameters, such as a chain with reservoirs at left and right ends. - lang: fre text: Nous considérons des processus d’exclusion partielle, et des processus d’inclusion sur un graphe général en contact avec des réservoirs. Nous autorisons la présence de inhomogenéités sur les arrêts ainsi que sur les sommets du graph. Nous généralisons les “dualités classiques” dans ce contexte et nous démontrons des nouvelles dualités orthogonales. À partir des dualités classiques, nous démontrons l’unicité de l’état stationnaire non-équilibre, ainsi que des inégalités de corrélation. À partir des dualités orthogonales nous démontrons des propriétés universelles des fonctions de corrélation à n points dans l’état stationnaire non-équilibre pour des systèmes avec deux paramètres de réservoirs inégaux, comme par exemple une chaîne avec des réservoirs à droite et à gauche. acknowledgement: The authors would like to thank Gioia Carinci and Cristian Giardinà for useful discussions. F.R. and S.F. thank Jean-René Chazottes for a stay at CPHT (Institut Polytechnique de Paris), in the realm of Chaire d’Alembert (Paris-Saclay University), where part of this work was performed. S.F. acknowledges Simona Villa for her support in creating the picture. S.F. acknowledges financial support from NWO via the grant TOP1.17.019. F.S. acknowledges financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411. article_processing_charge: No article_type: original author: - first_name: Simone full_name: Floreani, Simone last_name: Floreani - first_name: Frank full_name: Redig, Frank last_name: Redig - first_name: Federico full_name: Sau, Federico id: E1836206-9F16-11E9-8814-AEFDE5697425 last_name: Sau citation: ama: Floreani S, Redig F, Sau F. Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2022;58(1):220-247. doi:10.1214/21-AIHP1163 apa: Floreani, S., Redig, F., & Sau, F. (2022). Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AIHP1163 chicago: Floreani, Simone, Frank Redig, and Federico Sau. “Orthogonal Polynomial Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AIHP1163. ieee: S. Floreani, F. Redig, and F. Sau, “Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 58, no. 1. Institute of Mathematical Statistics, pp. 220–247, 2022. ista: Floreani S, Redig F, Sau F. 2022. Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. Annales de l’institut Henri Poincare (B) Probability and Statistics. 58(1), 220–247. mla: Floreani, Simone, et al. “Orthogonal Polynomial Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 58, no. 1, Institute of Mathematical Statistics, 2022, pp. 220–47, doi:10.1214/21-AIHP1163. short: S. Floreani, F. Redig, F. Sau, Annales de l’institut Henri Poincare (B) Probability and Statistics 58 (2022) 220–247. date_created: 2022-02-27T23:01:50Z date_published: 2022-02-01T00:00:00Z date_updated: 2023-10-17T12:49:43Z day: '01' department: - _id: JaMa doi: 10.1214/21-AIHP1163 ec_funded: 1 external_id: arxiv: - '2007.08272' isi: - '000752489300010' intvolume: ' 58' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2007.08272 month: '02' oa: 1 oa_version: Preprint page: 220-247 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Annales de l'institut Henri Poincare (B) Probability and Statistics publication_identifier: issn: - 0246-0203 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 58 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 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: '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 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: '10613' abstract: - lang: eng text: Motivated by the recent preprint [\emph{arXiv:2004.08412}] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher-order fields. Then, by considering the same class of infinite interacting particle systems as in [\emph{arXiv:2004.08412}], namely symmetric simple exclusion and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}], since we considered-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}], since we consider a different notion of higher-order fluctuation fields. acknowledgement: "F.S. would like to thank Mario Ayala and Frank Redig for useful discussions. J.P.C. acknowledges partial financial support from the US National Science Foundation (DMS-1855604). F.S. was financially supported by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.\r\n" article_processing_charge: No article_type: original author: - first_name: Joe P. full_name: Chen, Joe P. last_name: Chen - first_name: Federico full_name: Sau, Federico id: E1836206-9F16-11E9-8814-AEFDE5697425 last_name: Sau citation: ama: Chen JP, Sau F. Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. Markov Processes And Related Fields. 2021;27(3):339-380. apa: Chen, J. P., & Sau, F. (2021). Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. Markov Processes And Related Fields. Polymat Publishing. chicago: Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems.” Markov Processes And Related Fields. Polymat Publishing, 2021. ieee: J. P. Chen and F. Sau, “Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems,” Markov Processes And Related Fields, vol. 27, no. 3. Polymat Publishing, pp. 339–380, 2021. ista: Chen JP, Sau F. 2021. Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. Markov Processes And Related Fields. 27(3), 339–380. mla: Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems.” Markov Processes And Related Fields, vol. 27, no. 3, Polymat Publishing, 2021, pp. 339–80. short: J.P. Chen, F. Sau, Markov Processes And Related Fields 27 (2021) 339–380. date_created: 2022-01-10T14:02:31Z date_published: 2021-03-16T00:00:00Z date_updated: 2022-01-10T15:29:08Z day: '16' department: - _id: JaMa ec_funded: 1 external_id: arxiv: - '2008.13403' intvolume: ' 27' issue: '3' keyword: - interacting particle systems - higher-order fields - hydrodynamic limit - equilibrium fluctuations - duality language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2008.13403 month: '03' oa: 1 oa_version: Preprint page: 339-380 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Markov Processes And Related Fields publication_identifier: issn: - 1024-2953 publication_status: published publisher: Polymat Publishing quality_controlled: '1' related_material: link: - description: Link to Abstract on publisher's website relation: other url: http://math-mprf.org/journal/articles/id1614/ - description: Referred to in Abstract relation: used_for_analysis_in url: https://arxiv.org/abs/2004.08412 status: public title: Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems type: journal_article user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 27 year: '2021' ... --- _id: '9973' abstract: - lang: eng text: In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors. acknowledgement: Both authors would like to thank Jan Maas for fruitful discussions and helpful comments. 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 - first_name: Haonan full_name: Zhang, Haonan id: D8F41E38-9E66-11E9-A9E2-65C2E5697425 last_name: Zhang citation: ama: Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 2021;387:761–791. doi:10.1007/s00220-021-04199-4 apa: Wirth, M., & Zhang, H. (2021). Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04199-4 chicago: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04199-4. ieee: M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,” Communications in Mathematical Physics, vol. 387. Springer Nature, pp. 761–791, 2021. ista: Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791. mla: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” Communications in Mathematical Physics, vol. 387, Springer Nature, 2021, pp. 761–791, doi:10.1007/s00220-021-04199-4. short: M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791. date_created: 2021-08-30T10:07:44Z date_published: 2021-08-30T00:00:00Z date_updated: 2023-08-11T11:09:07Z day: '30' ddc: - '621' department: - _id: JaMa doi: 10.1007/s00220-021-04199-4 ec_funded: 1 external_id: arxiv: - '2007.13506' isi: - '000691214200001' file: - access_level: open_access checksum: 8a602f916b1c2b0dc1159708b7cb204b content_type: application/pdf creator: cchlebak date_created: 2021-09-08T07:34:24Z date_updated: 2021-09-08T09:46:34Z file_id: '9990' file_name: 2021_CommunMathPhys_Wirth.pdf file_size: 505971 relation: main_file file_date_updated: 2021-09-08T09:46:34Z has_accepted_license: '1' intvolume: ' 387' isi: 1 keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: 761–791 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Complete gradient estimates of 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 387 year: '2021' ... --- _id: '10024' abstract: - lang: eng text: In this paper, we introduce a random environment for the exclusion process in obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we derive a quenched hydrodynamic limit in path space by strengthening the mild solution approach initiated in Nagy (2002) and Faggionato (2007). To this purpose, we prove, employing the technology developed for the random conductance model, a homogenization result in the form of an arbitrary starting point quenched invariance principle for a single particle in the same environment, which is a result of independent interest. The self-duality property of the partial exclusion process allows us to transfer this homogenization result to the particle system and, then, apply the tightness criterion in Redig et al. (2020). acknowledgement: The authors would like to thank Marek Biskup and Alberto Chiarini for useful suggestions and Cristian Giardina, Frank den Hollander and Shubhamoy Nandan for inspiring discussions. S.F. acknowledges Simona Villa for her help in creating the picture. Furthermore, the authors thank two anonymous referees for the careful reading of the manuscript. S.F. acknowledges financial support from NWO, The Netherlands via the grant TOP1.17.019. F.S. acknowledges financial support from NWO via the TOP1 grant 613.001.552 as well as funding from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411. article_processing_charge: Yes article_type: original author: - first_name: Simone full_name: Floreani, Simone last_name: Floreani - first_name: Frank full_name: Redig, Frank last_name: Redig - first_name: Federico full_name: Sau, Federico id: E1836206-9F16-11E9-8814-AEFDE5697425 last_name: Sau citation: ama: Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 2021;142:124-158. doi:10.1016/j.spa.2021.08.006 apa: Floreani, S., Redig, F., & Sau, F. (2021). Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and Their Applications. Elsevier. https://doi.org/10.1016/j.spa.2021.08.006 chicago: Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” Stochastic Processes and Their Applications. Elsevier, 2021. https://doi.org/10.1016/j.spa.2021.08.006. ieee: S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion process in random environment,” Stochastic Processes and their Applications, vol. 142. Elsevier, pp. 124–158, 2021. ista: Floreani S, Redig F, Sau F. 2021. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 142, 124–158. mla: Floreani, Simone, et al. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” Stochastic Processes and Their Applications, vol. 142, Elsevier, 2021, pp. 124–58, doi:10.1016/j.spa.2021.08.006. short: S. Floreani, F. Redig, F. Sau, Stochastic Processes and Their Applications 142 (2021) 124–158. date_created: 2021-09-19T22:01:25Z date_published: 2021-08-27T00:00:00Z date_updated: 2023-08-14T06:52:43Z day: '27' ddc: - '519' department: - _id: JaMa doi: 10.1016/j.spa.2021.08.006 ec_funded: 1 external_id: arxiv: - '1911.12564' isi: - '000697748500005' file: - access_level: open_access checksum: 56768c553d7218ee5714902ffec90ec4 content_type: application/pdf creator: dernst date_created: 2022-05-13T07:55:50Z date_updated: 2022-05-13T07:55:50Z file_id: '11370' file_name: 2021_StochasticProcessesAppl_Floreani.pdf file_size: 2115791 relation: main_file success: 1 file_date_updated: 2022-05-13T07:55:50Z has_accepted_license: '1' intvolume: ' 142' isi: 1 keyword: - hydrodynamic limit - random environment - random conductance model - arbitrary starting point quenched invariance principle - duality - mild solution language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: 124-158 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Stochastic Processes and their Applications publication_identifier: issn: - 0304-4149 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Hydrodynamics for the partial exclusion process in random environment 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: 142 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 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: '9627' abstract: - lang: eng text: "We compute the deficiency spaces of operators of the form \U0001D43B\U0001D434⊗̂ \U0001D43C+\U0001D43C⊗̂ \U0001D43B\U0001D435, for symmetric \U0001D43B\U0001D434 and self-adjoint \U0001D43B\U0001D435. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301], but only proven under the restriction of \U0001D43B\U0001D435 having discrete, non-degenerate spectrum." acknowledgement: M. W. gratefully acknowledges financial support by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes). T.W. thanks PAO Gazprom Neft, the Euler International Mathematical Institute in Saint Petersburg and ORISA GmbH for their financial support in the form of scholarships during his Master's and Bachelor's studies respectively. The authors want to thank Mark Malamud for pointing out the reference [1] to them. This work was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No 075-15-2019-1619. article_processing_charge: No article_type: original author: - first_name: Daniel full_name: Lenz, Daniel last_name: Lenz - first_name: Timon full_name: Weinmann, Timon last_name: Weinmann - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 citation: ama: Lenz D, Weinmann T, Wirth M. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 2021;64(3):443-447. doi:10.1017/S0013091521000080 apa: Lenz, D., Weinmann, T., & Wirth, M. (2021). Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. Cambridge University Press. https://doi.org/10.1017/S0013091521000080 chicago: Lenz, Daniel, Timon Weinmann, and Melchior Wirth. “Self-Adjoint Extensions of Bipartite Hamiltonians.” Proceedings of the Edinburgh Mathematical Society. Cambridge University Press, 2021. https://doi.org/10.1017/S0013091521000080. ieee: D. Lenz, T. Weinmann, and M. Wirth, “Self-adjoint extensions of bipartite Hamiltonians,” Proceedings of the Edinburgh Mathematical Society, vol. 64, no. 3. Cambridge University Press, pp. 443–447, 2021. ista: Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447. mla: Lenz, Daniel, et al. “Self-Adjoint Extensions of Bipartite Hamiltonians.” Proceedings of the Edinburgh Mathematical Society, vol. 64, no. 3, Cambridge University Press, 2021, pp. 443–47, doi:10.1017/S0013091521000080. short: D. Lenz, T. Weinmann, M. Wirth, Proceedings of the Edinburgh Mathematical Society 64 (2021) 443–447. date_created: 2021-07-04T22:01:24Z date_published: 2021-08-01T00:00:00Z date_updated: 2023-08-17T07:12:05Z day: '01' department: - _id: JaMa doi: 10.1017/S0013091521000080 external_id: arxiv: - '1912.03670' isi: - '000721363700003' intvolume: ' 64' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1017/S0013091521000080 month: '08' oa: 1 oa_version: Published Version page: 443-447 publication: Proceedings of the Edinburgh Mathematical Society publication_identifier: eissn: - 1464-3839 issn: - 0013-0915 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Self-adjoint extensions of bipartite Hamiltonians type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 64 year: '2021' ... --- _id: '10030' abstract: - lang: eng text: "This PhD thesis is primarily focused on the study of discrete transport problems, introduced for the first time in the seminal works of Maas [Maa11] and Mielke [Mie11] on finite state Markov chains and reaction-diffusion equations, respectively. More in detail, my research focuses on the study of transport costs on graphs, in particular the convergence and the stability of such problems in the discrete-to-continuum limit. This thesis also includes some results concerning\r\nnon-commutative optimal transport. The first chapter of this thesis consists of a general introduction to the optimal transport problems, both in the discrete, the continuous, and the non-commutative setting. Chapters 2 and 3 present the content of two works, obtained in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have been able to show the convergence of discrete transport costs on periodic graphs to suitable continuous ones, which can be described by means of a homogenisation result. We first focus on the particular case of quadratic costs on the real line and then extending the result to more general costs in arbitrary dimension. Our results are the first complete characterisation of limits of transport costs on periodic graphs in arbitrary dimension which do not rely on any additional symmetry. In Chapter 4 we turn our attention to one of the intriguing connection between evolution equations and optimal transport, represented by the theory of gradient flows. We show that discrete gradient flow structures associated to a finite volume approximation of a certain class of diffusive equations (Fokker–Planck) is stable in the limit of vanishing meshes, reproving the convergence of the scheme via the method of evolutionary Γ-convergence and exploiting a more variational point of view on the problem. This is based on a collaboration with Dominik Forkert and Jan Maas. Chapter 5 represents a change of perspective, moving away from the discrete world and reaching the non-commutative one. As in the discrete case, we discuss how classical tools coming from the commutative optimal transport can be translated into the setting of density matrices. In particular, in this final chapter we present a non-commutative version of the Schrödinger problem (or entropic regularised optimal transport problem) and discuss existence and characterisation of minimisers, a duality result, and present a non-commutative version of the well-known Sinkhorn algorithm to compute the above mentioned optimisers. This is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally, Appendix A and B contain some additional material and discussions, with particular attention to Harnack inequalities and the regularity of flows on discrete spaces." acknowledged_ssus: - _id: M-Shop - _id: NanoFab acknowledgement: The author gratefully acknowledges support by the Austrian Science Fund (FWF), grants No W1245. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: ama: Portinale L. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. 2021. doi:10.15479/at:ista:10030 apa: Portinale, L. (2021). Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:10030 chicago: Portinale, Lorenzo. “Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:10030. ieee: L. Portinale, “Discrete-to-continuum limits of transport problems and gradient flows in the space of measures,” Institute of Science and Technology Austria, 2021. ista: Portinale L. 2021. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. Institute of Science and Technology Austria. mla: Portinale, Lorenzo. Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:10030. short: L. Portinale, Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures, Institute of Science and Technology Austria, 2021. date_created: 2021-09-21T09:14:15Z date_published: 2021-09-22T00:00:00Z date_updated: 2023-09-07T13:31:06Z day: '22' ddc: - '515' degree_awarded: PhD department: - _id: GradSch - _id: JaMa doi: 10.15479/at:ista:10030 file: - access_level: closed checksum: 8cd60dcb8762e8f21867e21e8001e183 content_type: application/x-zip-compressed creator: cchlebak date_created: 2021-09-21T09:17:34Z date_updated: 2022-03-10T12:14:42Z file_id: '10032' file_name: tex_and_pictures.zip file_size: 3876668 relation: source_file - access_level: open_access checksum: 9789e9d967c853c1503ec7f307170279 content_type: application/pdf creator: cchlebak date_created: 2021-09-27T11:14:31Z date_updated: 2021-09-27T11:14:31Z file_id: '10047' file_name: thesis_portinale_Final (1).pdf file_size: 2532673 relation: main_file file_date_updated: 2022-03-10T12:14:42Z has_accepted_license: '1' language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: 260788DE-B435-11E9-9278-68D0E5697425 call_identifier: FWF name: Dissipation and Dispersion in Nonlinear Partial Differential Equations - _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: '10022' relation: part_of_dissertation status: public - id: '9792' relation: part_of_dissertation status: public - id: '7573' relation: part_of_dissertation status: public 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: Discrete-to-continuum limits of transport problems and gradient flows in the space of measures 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: 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 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: '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 license: https://creativecommons.org/licenses/by-nd/4.0/ 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: '6358' abstract: - lang: eng text: We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Eric A. full_name: Carlen, Eric A. last_name: Carlen - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 citation: ama: Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. Journal of Statistical Physics. 2020;178(2):319-378. doi:10.1007/s10955-019-02434-w apa: Carlen, E. A., & Maas, J. (2020). Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-019-02434-w chicago: Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems.” Journal of Statistical Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-019-02434-w. ieee: E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems,” Journal of Statistical Physics, vol. 178, no. 2. Springer Nature, pp. 319–378, 2020. ista: Carlen EA, Maas J. 2020. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. Journal of Statistical Physics. 178(2), 319–378. mla: Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems.” Journal of Statistical Physics, vol. 178, no. 2, Springer Nature, 2020, pp. 319–78, doi:10.1007/s10955-019-02434-w. short: E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378. date_created: 2019-04-30T07:34:18Z date_published: 2020-01-01T00:00:00Z date_updated: 2023-08-17T13:49:40Z day: '01' ddc: - '500' department: - _id: JaMa doi: 10.1007/s10955-019-02434-w ec_funded: 1 external_id: arxiv: - '1811.04572' isi: - '000498933300001' file: - access_level: open_access checksum: 7b04befbdc0d4982c0ee945d25d19872 content_type: application/pdf creator: dernst date_created: 2019-12-23T12:03:09Z date_updated: 2020-07-14T12:47:28Z file_id: '7209' file_name: 2019_JourStatistPhysics_Carlen.pdf file_size: 905538 relation: main_file file_date_updated: 2020-07-14T12:47:28Z has_accepted_license: '1' intvolume: ' 178' isi: 1 issue: '2' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 319-378 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _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' related_material: link: - relation: erratum url: https://doi.org/10.1007/s10955-020-02671-4 scopus_import: '1' status: public title: Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems 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: 178 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 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: '7388' abstract: - lang: eng text: We give a Wong-Zakai type characterisation of the solutions of quasilinear heat equations driven by space-time white noise in 1 + 1 dimensions. In order to show that the renormalisation counterterms are local in the solution, a careful arrangement of a few hundred terms is required. The main tool in this computation is a general ‘integration by parts’ formula that provides a number of linear identities for the renormalisation constants. article_processing_charge: No article_type: original author: - first_name: Mate full_name: Gerencser, Mate id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87 last_name: Gerencser citation: ama: Gerencser M. Nondivergence form quasilinear heat equations driven by space-time white noise. Annales de l’Institut Henri Poincaré C, Analyse non linéaire. 2020;37(3):663-682. doi:10.1016/j.anihpc.2020.01.003 apa: Gerencser, M. (2020). Nondivergence form quasilinear heat equations driven by space-time white noise. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire. Elsevier. https://doi.org/10.1016/j.anihpc.2020.01.003 chicago: Gerencser, Mate. “Nondivergence Form Quasilinear Heat Equations Driven by Space-Time White Noise.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire. Elsevier, 2020. https://doi.org/10.1016/j.anihpc.2020.01.003. ieee: M. Gerencser, “Nondivergence form quasilinear heat equations driven by space-time white noise,” Annales de l’Institut Henri Poincaré C, Analyse non linéaire, vol. 37, no. 3. Elsevier, pp. 663–682, 2020. ista: Gerencser M. 2020. Nondivergence form quasilinear heat equations driven by space-time white noise. Annales de l’Institut Henri Poincaré C, Analyse non linéaire. 37(3), 663–682. mla: Gerencser, Mate. “Nondivergence Form Quasilinear Heat Equations Driven by Space-Time White Noise.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, vol. 37, no. 3, Elsevier, 2020, pp. 663–82, doi:10.1016/j.anihpc.2020.01.003. short: M. Gerencser, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 37 (2020) 663–682. date_created: 2020-01-29T09:39:41Z date_published: 2020-05-01T00:00:00Z date_updated: 2023-08-17T14:35:46Z day: '01' department: - _id: JaMa doi: 10.1016/j.anihpc.2020.01.003 external_id: arxiv: - '1902.07635' isi: - '000531049800007' intvolume: ' 37' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1902.07635 month: '05' oa: 1 oa_version: Preprint page: 663-682 publication: Annales de l'Institut Henri Poincaré C, Analyse non linéaire publication_identifier: issn: - 0294-1449 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Nondivergence form quasilinear heat equations driven by space-time white noise type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 37 year: '2020' ... --- _id: '7509' abstract: - lang: eng text: "In this paper we study the joint convexity/concavity of the trace functions Ψp,q,s(A,B)=Tr(Bq2K∗ApKBq2)s, p,q,s∈R,\r\nwhere A and B are positive definite matrices and K is any fixed invertible matrix. We will give full range of (p,q,s)∈R3 for Ψp,q,s to be jointly convex/concave for all K. As a consequence, we confirm a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture of Audenaert and Datta and obtain the full range of (α,z) for α-z Rényi relative entropies to be monotone under completely positive trace preserving maps. We also give simpler proofs of many known results, including the concavity of Ψp,0,1/p for 0Advances in Mathematics. 2020;365. doi:10.1016/j.aim.2020.107053 apa: Zhang, H. (2020). From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2020.107053 chicago: Zhang, Haonan. “From Wigner-Yanase-Dyson Conjecture to Carlen-Frank-Lieb Conjecture.” Advances in Mathematics. Elsevier, 2020. https://doi.org/10.1016/j.aim.2020.107053. ieee: H. Zhang, “From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture,” Advances in Mathematics, vol. 365. Elsevier, 2020. ista: Zhang H. 2020. From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics. 365, 107053. mla: Zhang, Haonan. “From Wigner-Yanase-Dyson Conjecture to Carlen-Frank-Lieb Conjecture.” Advances in Mathematics, vol. 365, 107053, Elsevier, 2020, doi:10.1016/j.aim.2020.107053. short: H. Zhang, Advances in Mathematics 365 (2020). date_created: 2020-02-23T21:43:50Z date_published: 2020-05-13T00:00:00Z date_updated: 2023-08-18T06:37:09Z day: '13' ddc: - '515' department: - _id: JaMa doi: 10.1016/j.aim.2020.107053 ec_funded: 1 external_id: arxiv: - '1811.01205' isi: - '000522798000001' intvolume: ' 365' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1811.01205 month: '05' oa: 1 oa_version: Preprint project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Advances in Mathematics publication_status: published publisher: Elsevier quality_controlled: '1' status: public title: From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 365 year: '2020' ... --- _id: '8670' abstract: - lang: eng text: The α–z Rényi relative entropies are a two-parameter family of Rényi relative entropies that are quantum generalizations of the classical α-Rényi relative entropies. In the work [Adv. Math. 365, 107053 (2020)], we decided the full range of (α, z) for which the data processing inequality (DPI) is valid. In this paper, we give algebraic conditions for the equality in DPI. For the full range of parameters (α, z), we give necessary conditions and sufficient conditions. For most parameters, we give equivalent conditions. This generalizes and strengthens the results of Leditzky et al. [Lett. Math. Phys. 107, 61–80 (2017)]. acknowledgement: This research was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 754411. The author would like to thank Anna Vershynina and Sarah Chehade for their helpful comments. article_number: '102201' article_processing_charge: No article_type: original author: - first_name: Haonan full_name: Zhang, Haonan id: D8F41E38-9E66-11E9-A9E2-65C2E5697425 last_name: Zhang citation: ama: Zhang H. Equality conditions of data processing inequality for α-z Rényi relative entropies. Journal of Mathematical Physics. 2020;61(10). doi:10.1063/5.0022787 apa: Zhang, H. (2020). Equality conditions of data processing inequality for α-z Rényi relative entropies. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0022787 chicago: Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z Rényi Relative Entropies.” Journal of Mathematical Physics. AIP Publishing, 2020. https://doi.org/10.1063/5.0022787. ieee: H. Zhang, “Equality conditions of data processing inequality for α-z Rényi relative entropies,” Journal of Mathematical Physics, vol. 61, no. 10. AIP Publishing, 2020. ista: Zhang H. 2020. Equality conditions of data processing inequality for α-z Rényi relative entropies. Journal of Mathematical Physics. 61(10), 102201. mla: Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z Rényi Relative Entropies.” Journal of Mathematical Physics, vol. 61, no. 10, 102201, AIP Publishing, 2020, doi:10.1063/5.0022787. short: H. Zhang, Journal of Mathematical Physics 61 (2020). date_created: 2020-10-18T22:01:36Z date_published: 2020-10-01T00:00:00Z date_updated: 2023-08-22T10:32:29Z day: '01' department: - _id: JaMa doi: 10.1063/5.0022787 ec_funded: 1 external_id: arxiv: - '2007.06644' isi: - '000578529200001' intvolume: ' 61' isi: 1 issue: '10' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2007.06644 month: '10' oa: 1 oa_version: Preprint project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Mathematical Physics publication_identifier: issn: - '00222488' publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Equality conditions of data processing inequality for α-z Rényi relative entropies type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 61 year: '2020' ... --- _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 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: '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' ...