[{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"12216","ddc":["510"],"status":"public","title":"Monotonicity versions of Epstein's concavity theorem and related inequalities","intvolume":" 654","oa_version":"Published Version","file":[{"success":1,"checksum":"cf3cb7e7e34baa967849f01d8f0c1ae4","date_created":"2023-01-27T08:08:39Z","date_updated":"2023-01-27T08:08:39Z","file_id":"12415","relation":"main_file","creator":"dernst","file_size":441184,"content_type":"application/pdf","access_level":"open_access","file_name":"2022_LinearAlgebra_Carlen.pdf"}],"type":"journal_article","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."}],"publication":"Linear Algebra and its Applications","citation":{"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.","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.","ista":"Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 654, 289–310.","ieee":"E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem and related inequalities,” Linear Algebra and its Applications, vol. 654. Elsevier, pp. 289–310, 2022.","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","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"},"article_type":"original","page":"289-310","date_published":"2022-12-01T00:00:00Z","scopus_import":"1","keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Numerical Analysis","Algebra and Number Theory"],"day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","year":"2022","acknowledgement":"Work partially supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.","publication_status":"published","publisher":"Elsevier","department":[{"_id":"JaMa"}],"author":[{"full_name":"Carlen, Eric A.","first_name":"Eric A.","last_name":"Carlen"},{"first_name":"Haonan","last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan"}],"date_created":"2023-01-16T09:46:38Z","date_updated":"2023-08-04T09:24:51Z","volume":654,"file_date_updated":"2023-01-27T08:08:39Z","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000860689600014"]},"isi":1,"quality_controlled":"1","project":[{"name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"}],"doi":"10.1016/j.laa.2022.09.001","language":[{"iso":"eng"}],"month":"12","publication_identifier":{"issn":["0024-3795"]}},{"language":[{"iso":"eng"}],"doi":"10.3150/21-bej1390","quality_controlled":"1","isi":1,"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"external_id":{"isi":["000766619100025"],"arxiv":["2007.11998"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2007.11998","open_access":"1"}],"oa":1,"month":"05","publication_identifier":{"issn":["1350-7265"]},"date_created":"2023-01-16T10:03:04Z","date_updated":"2023-08-04T10:27:35Z","volume":28,"author":[{"first_name":"Chiara","last_name":"Franceschini","full_name":"Franceschini, Chiara"},{"first_name":"Patrícia","last_name":"Gonçalves","full_name":"Gonçalves, Patrícia"},{"last_name":"Sau","first_name":"Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425","full_name":"Sau, Federico"}],"publication_status":"published","publisher":"Bernoulli Society for Mathematical Statistics and Probability","department":[{"_id":"JaMa"}],"year":"2022","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.","ec_funded":1,"date_published":"2022-05-01T00:00:00Z","article_type":"original","page":"1340-1381","publication":"Bernoulli","citation":{"ista":"Franceschini C, Gonçalves P, Sau F. 2022. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 28(2), 1340–1381.","ieee":"C. Franceschini, P. Gonçalves, and F. Sau, “Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics,” Bernoulli, vol. 28, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1340–1381, 2022.","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","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","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.","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."},"day":"01","article_processing_charge":"No","keyword":["Statistics and Probability"],"scopus_import":"1","oa_version":"Preprint","status":"public","title":"Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics","intvolume":" 28","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"12281","abstract":[{"text":"We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary conditions as hydrodynamic equation. In our approach, we combine duality and first-second class particle techniques to reduce the scaling limit of the inclusion process to the limiting behavior of a single, non-interacting, particle.","lang":"eng"}],"issue":"2","type":"journal_article"},{"date_published":"2022-02-01T00:00:00Z","article_type":"original","page":"220-247","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","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","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.","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","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.","short":"S. Floreani, F. Redig, F. Sau, Annales de l’institut Henri Poincare (B) Probability and Statistics 58 (2022) 220–247.","mla":"Floreani, Simone, et al. “Orthogonal Polynomial Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 58, no. 1, Institute of Mathematical Statistics, 2022, pp. 220–47, doi:10.1214/21-AIHP1163.","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."},"day":"01","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","title":"Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations","status":"public","intvolume":" 58","_id":"10797","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then we derive new orthogonal polynomial dualities. From the classical dualities, we derive the uniqueness of the non-equilibrium steady state and obtain correlation inequalities. Starting from the orthogonal polynomial dualities, we show universal properties of n-point correlation functions in the non-equilibrium steady state for systems with at most two different reservoir parameters, such as a chain with reservoirs at left and right ends.","lang":"eng"},{"lang":"fre","text":"Nous considérons des processus d’exclusion partielle, et des processus d’inclusion sur un graphe général en contact avec des réservoirs. Nous autorisons la présence de inhomogenéités sur les arrêts ainsi que sur les sommets du graph. Nous généralisons les “dualités classiques” dans ce contexte et nous démontrons des nouvelles dualités orthogonales. À partir des dualités classiques, nous démontrons l’unicité de l’état stationnaire non-équilibre, ainsi que des inégalités de corrélation. À partir des dualités orthogonales nous démontrons des propriétés universelles des fonctions de corrélation à n points dans l’état stationnaire non-équilibre pour des systèmes avec deux paramètres de réservoirs inégaux, comme par exemple une chaîne avec des réservoirs à droite et à gauche."}],"issue":"1","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1214/21-AIHP1163","quality_controlled":"1","isi":1,"project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2007.08272"}],"external_id":{"arxiv":["2007.08272"],"isi":["000752489300010"]},"month":"02","publication_identifier":{"issn":["0246-0203"]},"date_created":"2022-02-27T23:01:50Z","date_updated":"2023-10-17T12:49:43Z","volume":58,"author":[{"last_name":"Floreani","first_name":"Simone","full_name":"Floreani, Simone"},{"full_name":"Redig, Frank","first_name":"Frank","last_name":"Redig"},{"last_name":"Sau","first_name":"Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425","full_name":"Sau, Federico"}],"publication_status":"published","department":[{"_id":"JaMa"}],"publisher":"Institute of Mathematical Statistics","acknowledgement":"The authors would like to thank Gioia Carinci and Cristian Giardinà for useful discussions. F.R. and S.F. thank Jean-René Chazottes for a stay at CPHT (Institut Polytechnique de Paris), in the realm of Chaire d’Alembert (Paris-Saclay University), where part of this work was performed. S.F. acknowledges Simona Villa for her support in creating the picture. S.F. acknowledges financial support from NWO via the grant TOP1.17.019. F.S. acknowledges financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.","year":"2022","ec_funded":1},{"publication_status":"published","publisher":"Institute of Mathematical Statistics","department":[{"_id":"JaMa"}],"acknowledgement":"Research supported by the Sonderforschungsbereich 1060 and the Hausdorff Center for Mathematics. The author gratefully acknowledges funding of his current position at IST Austria by the Austrian Science Fund (FWF) grant F65 and by the European Research Council (ERC, Grant agreement No. 716117, awarded to Prof. Dr. Jan Maas).","year":"2022","date_updated":"2023-10-17T12:50:24Z","date_created":"2022-05-08T22:01:44Z","volume":50,"author":[{"first_name":"Lorenzo","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo"}],"ec_funded":1,"isi":1,"quality_controlled":"1","project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"external_id":{"isi":["000773518500005"],"arxiv":["1811.11598"]},"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.1811.11598"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1214/21-AOP1541","month":"03","publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"title":"The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold","status":"public","intvolume":" 50","_id":"11354","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","type":"journal_article","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."}],"issue":"2","article_type":"original","page":"591-648","publication":"Annals of Probability","citation":{"chicago":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1541.","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.","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.","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","ieee":"L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold,” Annals of Probability, vol. 50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.","ama":"Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. 2022;50(2):591-648. doi:10.1214/21-AOP1541"},"date_published":"2022-03-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No"},{"abstract":[{"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.","lang":"eng"}],"issue":"4","type":"journal_article","oa_version":"Preprint","title":"Trajectorial dissipation and gradient flow for the relative entropy in Markov chains","status":"public","intvolume":" 21","_id":"10023","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","day":"04","article_processing_charge":"No","keyword":["Markov Chain","relative entropy","time reversal","steepest descent","gradient flow"],"date_published":"2021-06-04T00:00:00Z","article_type":"original","page":"481-536","publication":"Communications in Information and Systems","citation":{"short":"I. Karatzas, J. Maas, W. Schachermayer, Communications in Information and Systems 21 (2021) 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.","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.","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","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."},"ec_funded":1,"date_updated":"2021-09-20T12:51:18Z","date_created":"2021-09-19T08:53:19Z","volume":21,"author":[{"full_name":"Karatzas, Ioannis","first_name":"Ioannis","last_name":"Karatzas"},{"last_name":"Maas","first_name":"Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan"},{"last_name":"Schachermayer","first_name":"Walter","full_name":"Schachermayer, Walter"}],"publication_status":"published","department":[{"_id":"JaMa"}],"publisher":"International Press","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.","year":"2021","month":"06","publication_identifier":{"issn":["1526-7555"]},"language":[{"iso":"eng"}],"doi":"10.4310/CIS.2021.v21.n4.a1","quality_controlled":"1","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2005.14177"}],"external_id":{"arxiv":["2005.14177"]},"oa":1}]