[{"acknowledgement":"Work partially supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.","publisher":"Elsevier","quality_controlled":"1","oa":1,"isi":1,"has_accepted_license":"1","year":"2022","day":"01","publication":"Linear Algebra and its Applications","page":"289-310","date_published":"2022-12-01T00:00:00Z","doi":"10.1016/j.laa.2022.09.001","date_created":"2023-01-16T09:46:38Z","project":[{"grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"}],"citation":{"ista":"Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 654, 289–310.","chicago":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” Linear Algebra and Its Applications. Elsevier, 2022. https://doi.org/10.1016/j.laa.2022.09.001.","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","short":"E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.","ieee":"E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem and related inequalities,” Linear Algebra and its Applications, vol. 654. Elsevier, pp. 289–310, 2022.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Carlen, Eric A.","last_name":"Carlen","first_name":"Eric A."},{"first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","last_name":"Zhang","full_name":"Zhang, Haonan"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000860689600014"]},"title":"Monotonicity versions of Epstein's concavity theorem and related inequalities","abstract":[{"lang":"eng","text":"Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments."}],"oa_version":"Published Version","scopus_import":"1","month":"12","intvolume":" 654","publication_identifier":{"issn":["0024-3795"]},"publication_status":"published","file":[{"success":1,"checksum":"cf3cb7e7e34baa967849f01d8f0c1ae4","file_id":"12415","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2022_LinearAlgebra_Carlen.pdf","date_created":"2023-01-27T08:08:39Z","creator":"dernst","file_size":441184,"date_updated":"2023-01-27T08:08:39Z"}],"language":[{"iso":"eng"}],"volume":654,"_id":"12216","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Numerical Analysis","Algebra and Number Theory"],"date_updated":"2023-08-04T09:24:51Z","ddc":["510"],"department":[{"_id":"JaMa"}],"file_date_updated":"2023-01-27T08:08:39Z"},{"doi":"10.3150/21-bej1390","date_published":"2022-05-01T00:00:00Z","date_created":"2023-01-16T10:03:04Z","page":"1340-1381","day":"01","publication":"Bernoulli","isi":1,"year":"2022","quality_controlled":"1","publisher":"Bernoulli Society for Mathematical Statistics and Probability","oa":1,"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.","title":"Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics","author":[{"full_name":"Franceschini, Chiara","last_name":"Franceschini","first_name":"Chiara"},{"last_name":"Gonçalves","full_name":"Gonçalves, Patrícia","first_name":"Patrícia"},{"full_name":"Sau, Federico","last_name":"Sau","first_name":"Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425"}],"external_id":{"arxiv":["2007.11998"],"isi":["000766619100025"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Franceschini C, Gonçalves P, Sau F. 2022. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 28(2), 1340–1381.","chicago":"Franceschini, Chiara, Patrícia Gonçalves, and Federico Sau. “Symmetric Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” Bernoulli. Bernoulli Society for Mathematical Statistics and Probability, 2022. https://doi.org/10.3150/21-bej1390.","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","short":"C. Franceschini, P. Gonçalves, F. Sau, Bernoulli 28 (2022) 1340–1381.","ieee":"C. Franceschini, P. Gonçalves, and F. Sau, “Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics,” Bernoulli, vol. 28, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1340–1381, 2022.","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."},"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"issue":"2","volume":28,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1350-7265"]},"publication_status":"published","month":"05","intvolume":" 28","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2007.11998"}],"oa_version":"Preprint","abstract":[{"text":"We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary conditions as hydrodynamic equation. In our approach, we combine duality and first-second class particle techniques to reduce the scaling limit of the inclusion process to the limiting behavior of a single, non-interacting, particle.","lang":"eng"}],"department":[{"_id":"JaMa"}],"date_updated":"2023-08-04T10:27:35Z","status":"public","keyword":["Statistics and Probability"],"type":"journal_article","article_type":"original","_id":"12281"},{"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.","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","day":"01","year":"2022","isi":1,"date_created":"2022-02-27T23:01:50Z","doi":"10.1214/21-AIHP1163","date_published":"2022-02-01T00:00:00Z","page":"220-247","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Floreani S, Redig F, Sau F. 2022. Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. Annales de l’institut Henri Poincare (B) Probability and Statistics. 58(1), 220–247.","chicago":"Floreani, Simone, Frank Redig, and Federico Sau. “Orthogonal Polynomial Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AIHP1163.","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","ieee":"S. Floreani, F. Redig, and F. Sau, “Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 58, no. 1. Institute of Mathematical Statistics, pp. 220–247, 2022.","short":"S. Floreani, F. Redig, F. Sau, Annales de l’institut Henri Poincare (B) Probability and Statistics 58 (2022) 220–247.","mla":"Floreani, Simone, et al. “Orthogonal Polynomial Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 58, no. 1, Institute of Mathematical Statistics, 2022, pp. 220–47, doi:10.1214/21-AIHP1163."},"title":"Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations","article_processing_charge":"No","external_id":{"isi":["000752489300010"],"arxiv":["2007.08272"]},"author":[{"first_name":"Simone","full_name":"Floreani, Simone","last_name":"Floreani"},{"last_name":"Redig","full_name":"Redig, Frank","first_name":"Frank"},{"last_name":"Sau","full_name":"Sau, Federico","first_name":"Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425"}],"oa_version":"Preprint","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."},{"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.","lang":"fre"}],"intvolume":" 58","month":"02","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2007.08272"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0246-0203"]},"ec_funded":1,"volume":58,"issue":"1","_id":"10797","status":"public","type":"journal_article","article_type":"original","date_updated":"2023-10-17T12:49:43Z","department":[{"_id":"JaMa"}]},{"citation":{"chicago":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1541.","ista":"Dello Schiavo L. 2022. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. 50(2), 591–648.","mla":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability, vol. 50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:10.1214/21-AOP1541.","short":"L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.","ieee":"L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold,” Annals of Probability, vol. 50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.","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","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"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo"}],"external_id":{"arxiv":["1811.11598"],"isi":["000773518500005"]},"article_processing_charge":"No","title":"The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"isi":1,"year":"2022","day":"01","publication":"Annals of Probability","page":"591-648","date_published":"2022-03-01T00:00:00Z","doi":"10.1214/21-AOP1541","date_created":"2022-05-08T22:01:44Z","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).","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"date_updated":"2023-10-17T12:50:24Z","department":[{"_id":"JaMa"}],"_id":"11354","type":"journal_article","article_type":"original","status":"public","publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":50,"issue":"2","ec_funded":1,"abstract":[{"text":"We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1811.11598","open_access":"1"}],"month":"03","intvolume":" 50"},{"article_processing_charge":"No","external_id":{"arxiv":["2005.14177"]},"author":[{"last_name":"Karatzas","full_name":"Karatzas, Ioannis","first_name":"Ioannis"},{"first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas"},{"last_name":"Schachermayer","full_name":"Schachermayer, Walter","first_name":"Walter"}],"title":"Trajectorial dissipation and gradient flow for the relative entropy in Markov chains","citation":{"ista":"Karatzas I, Maas J, Schachermayer W. 2021. Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. Communications in Information and Systems. 21(4), 481–536.","chicago":"Karatzas, Ioannis, Jan Maas, and Walter Schachermayer. “Trajectorial Dissipation and Gradient Flow for the Relative Entropy in Markov Chains.” Communications in Information and Systems. International Press, 2021. https://doi.org/10.4310/CIS.2021.v21.n4.a1.","ieee":"I. Karatzas, J. Maas, and W. Schachermayer, “Trajectorial dissipation and gradient flow for the relative entropy in Markov chains,” Communications in Information and Systems, vol. 21, no. 4. International Press, pp. 481–536, 2021.","short":"I. Karatzas, J. Maas, W. Schachermayer, Communications in Information and Systems 21 (2021) 481–536.","apa":"Karatzas, I., Maas, J., & Schachermayer, W. (2021). Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. Communications in Information and Systems. International Press. https://doi.org/10.4310/CIS.2021.v21.n4.a1","ama":"Karatzas I, Maas J, Schachermayer W. Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. Communications in Information and Systems. 2021;21(4):481-536. doi:10.4310/CIS.2021.v21.n4.a1","mla":"Karatzas, Ioannis, et al. “Trajectorial Dissipation and Gradient Flow for the Relative Entropy in Markov Chains.” Communications in Information and Systems, vol. 21, no. 4, International Press, 2021, pp. 481–536, doi:10.4310/CIS.2021.v21.n4.a1."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"page":"481-536","date_created":"2021-09-19T08:53:19Z","doi":"10.4310/CIS.2021.v21.n4.a1","date_published":"2021-06-04T00:00:00Z","year":"2021","publication":"Communications in Information and Systems","day":"04","oa":1,"publisher":"International Press","quality_controlled":"1","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.","department":[{"_id":"JaMa"}],"date_updated":"2021-09-20T12:51:18Z","type":"journal_article","article_type":"original","keyword":["Markov Chain","relative entropy","time reversal","steepest descent","gradient flow"],"status":"public","_id":"10023","ec_funded":1,"issue":"4","volume":21,"publication_status":"published","publication_identifier":{"issn":["1526-7555"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2005.14177"}],"intvolume":" 21","month":"06","abstract":[{"lang":"eng","text":"We study the temporal dissipation of variance and relative entropy for ergodic Markov Chains in continuous time, and compute explicitly the corresponding dissipation rates. These are identified, as is well known, in the case of the variance in terms of an appropriate Hilbertian norm; and in the case of the relative entropy, in terms of a Dirichlet form which morphs into a version of the familiar Fisher information under conditions of detailed balance. Here we obtain trajectorial versions of these results, valid along almost every path of the random motion and most transparent in the backwards direction of time. Martingale arguments and time reversal play crucial roles, as in the recent work of Karatzas, Schachermayer and Tschiderer for conservative diffusions. Extensions are developed to general “convex divergences” and to countable state-spaces. The steepest descent and gradient flow properties for the variance, the relative entropy, and appropriate generalizations, are studied along with their respective geometries under conditions of detailed balance, leading to a very direct proof for the HWI inequality of Otto and Villani in the present context."}],"oa_version":"Preprint"},{"ec_funded":1,"issue":"3","related_material":{"link":[{"description":"Link to Abstract on publisher's website","relation":"other","url":"http://math-mprf.org/journal/articles/id1614/"},{"relation":"used_for_analysis_in","url":"https://arxiv.org/abs/2004.08412","description":"Referred to in Abstract"}]},"volume":27,"publication_status":"published","publication_identifier":{"issn":["1024-2953"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/2008.13403","open_access":"1"}],"intvolume":" 27","month":"03","abstract":[{"text":"Motivated by the recent preprint [\\emph{arXiv:2004.08412}] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher-order fields. Then, by considering the same class of infinite interacting particle systems as in [\\emph{arXiv:2004.08412}], namely symmetric simple exclusion and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\\emph{arXiv:2004.08412}], since we considered-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\\emph{arXiv:2004.08412}], since we consider a different notion of higher-order fluctuation fields.","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"JaMa"}],"date_updated":"2022-01-10T15:29:08Z","type":"journal_article","article_type":"original","keyword":["interacting particle systems","higher-order fields","hydrodynamic limit","equilibrium fluctuations","duality"],"status":"public","_id":"10613","page":"339-380","date_created":"2022-01-10T14:02:31Z","date_published":"2021-03-16T00:00:00Z","year":"2021","publication":"Markov Processes And Related Fields","day":"16","oa":1,"quality_controlled":"1","publisher":"Polymat Publishing","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","external_id":{"arxiv":["2008.13403"]},"article_processing_charge":"No","author":[{"first_name":"Joe P.","full_name":"Chen, Joe P.","last_name":"Chen"},{"last_name":"Sau","full_name":"Sau, Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico"}],"title":"Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems","citation":{"ista":"Chen JP, Sau F. 2021. Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. Markov Processes And Related Fields. 27(3), 339–380.","chicago":"Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems.” Markov Processes And Related Fields. Polymat Publishing, 2021.","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.","ieee":"J. P. Chen and F. Sau, “Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems,” Markov Processes And Related Fields, vol. 27, no. 3. Polymat Publishing, pp. 339–380, 2021.","short":"J.P. Chen, F. Sau, Markov Processes And Related Fields 27 (2021) 339–380.","mla":"Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems.” Markov Processes And Related Fields, vol. 27, no. 3, Polymat Publishing, 2021, pp. 339–80."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}]},{"department":[{"_id":"JaMa"}],"file_date_updated":"2021-09-08T09:46:34Z","date_updated":"2023-08-11T11:09:07Z","ddc":["621"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"status":"public","_id":"9973","ec_funded":1,"volume":387,"publication_status":"published","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"language":[{"iso":"eng"}],"file":[{"date_created":"2021-09-08T07:34:24Z","file_name":"2021_CommunMathPhys_Wirth.pdf","creator":"cchlebak","date_updated":"2021-09-08T09:46:34Z","file_size":505971,"file_id":"9990","checksum":"8a602f916b1c2b0dc1159708b7cb204b","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"scopus_import":"1","intvolume":" 387","month":"08","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."}],"oa_version":"Published Version","external_id":{"arxiv":["2007.13506"],"isi":["000691214200001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Wirth","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"},{"first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan","last_name":"Zhang"}],"title":"Complete gradient estimates of quantum Markov semigroups","citation":{"chicago":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04199-4.","ista":"Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791.","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.","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","short":"M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"page":"761–791","date_created":"2021-08-30T10:07:44Z","doi":"10.1007/s00220-021-04199-4","date_published":"2021-08-30T00:00:00Z","year":"2021","isi":1,"has_accepted_license":"1","publication":"Communications in Mathematical Physics","day":"30","oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"Both authors would like to thank Jan Maas for fruitful discussions and helpful comments."},{"_id":"10024","keyword":["hydrodynamic limit","random environment","random conductance model","arbitrary starting point quenched invariance principle","duality","mild solution"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","ddc":["519"],"date_updated":"2023-08-14T06:52:43Z","department":[{"_id":"JaMa"}],"file_date_updated":"2022-05-13T07:55:50Z","oa_version":"Published Version","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)."}],"intvolume":" 142","month":"08","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"success":1,"checksum":"56768c553d7218ee5714902ffec90ec4","file_id":"11370","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2021_StochasticProcessesAppl_Floreani.pdf","date_created":"2022-05-13T07:55:50Z","creator":"dernst","file_size":2115791,"date_updated":"2022-05-13T07:55:50Z"}],"publication_status":"published","publication_identifier":{"issn":["0304-4149"]},"ec_funded":1,"volume":142,"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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.","apa":"Floreani, S., Redig, F., & Sau, F. (2021). Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and Their Applications. Elsevier. https://doi.org/10.1016/j.spa.2021.08.006","ama":"Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 2021;142:124-158. doi:10.1016/j.spa.2021.08.006","chicago":"Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” Stochastic Processes and Their Applications. Elsevier, 2021. https://doi.org/10.1016/j.spa.2021.08.006.","ista":"Floreani S, Redig F, Sau F. 2021. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 142, 124–158."},"title":"Hydrodynamics for the partial exclusion process in random environment","article_processing_charge":"Yes","external_id":{"isi":["000697748500005"],"arxiv":["1911.12564"]},"author":[{"full_name":"Floreani, Simone","last_name":"Floreani","first_name":"Simone"},{"last_name":"Redig","full_name":"Redig, Frank","first_name":"Frank"},{"first_name":"Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425","full_name":"Sau, Federico","last_name":"Sau"}],"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.","oa":1,"publisher":"Elsevier","quality_controlled":"1","publication":"Stochastic Processes and their Applications","day":"27","year":"2021","isi":1,"has_accepted_license":"1","date_created":"2021-09-19T22:01:25Z","date_published":"2021-08-27T00:00:00Z","doi":"10.1016/j.spa.2021.08.006","page":"124-158"},{"date_created":"2021-10-03T22:01:21Z","doi":"10.1016/j.jfa.2021.109234","date_published":"2021-09-15T00:00:00Z","year":"2021","isi":1,"publication":"Journal of Functional Analysis","day":"15","oa":1,"quality_controlled":"1","publisher":"Elsevier","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.","external_id":{"arxiv":["2008.01492"],"isi":["000703896600005"]},"article_processing_charge":"No","author":[{"full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo"},{"last_name":"Suzuki","full_name":"Suzuki, Kohei","first_name":"Kohei"}],"title":"Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces","citation":{"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.","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.","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","ieee":"L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces,” Journal of Functional Analysis, vol. 281, no. 11. Elsevier, 2021.","short":"L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}],"article_number":"109234","ec_funded":1,"issue":"11","volume":281,"publication_status":"published","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2008.01492","open_access":"1"}],"scopus_import":"1","intvolume":" 281","month":"09","abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"JaMa"}],"date_updated":"2023-08-14T07:05:44Z","article_type":"original","type":"journal_article","status":"public","_id":"10070"},{"date_created":"2021-07-04T22:01:24Z","date_published":"2021-08-01T00:00:00Z","doi":"10.1017/S0013091521000080","page":"443-447","publication":"Proceedings of the Edinburgh Mathematical Society","day":"01","year":"2021","isi":1,"oa":1,"quality_controlled":"1","publisher":"Cambridge University Press","acknowledgement":"M. W. gratefully acknowledges financial support by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes). T.W. thanks PAO Gazprom Neft, the Euler International Mathematical Institute in Saint Petersburg and ORISA GmbH for their financial support in the form of scholarships during his Master's and Bachelor's studies respectively. The authors want to thank Mark Malamud for pointing out the reference [1] to them. This work was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No 075-15-2019-1619.","title":"Self-adjoint extensions of bipartite Hamiltonians","article_processing_charge":"No","external_id":{"arxiv":["1912.03670"],"isi":["000721363700003"]},"author":[{"first_name":"Daniel","last_name":"Lenz","full_name":"Lenz, Daniel"},{"first_name":"Timon","full_name":"Weinmann, Timon","last_name":"Weinmann"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","first_name":"Melchior","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","last_name":"Wirth"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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","short":"D. Lenz, T. Weinmann, M. Wirth, Proceedings of the Edinburgh Mathematical Society 64 (2021) 443–447.","ieee":"D. Lenz, T. Weinmann, and M. Wirth, “Self-adjoint extensions of bipartite Hamiltonians,” Proceedings of the Edinburgh Mathematical Society, vol. 64, no. 3. Cambridge University Press, pp. 443–447, 2021.","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.","ista":"Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.","chicago":"Lenz, Daniel, Timon Weinmann, and Melchior Wirth. “Self-Adjoint Extensions of Bipartite Hamiltonians.” Proceedings of the Edinburgh Mathematical Society. Cambridge University Press, 2021. https://doi.org/10.1017/S0013091521000080."},"volume":64,"issue":"3","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0013-0915"],"eissn":["1464-3839"]},"intvolume":" 64","month":"08","main_file_link":[{"url":"https://doi.org/10.1017/S0013091521000080","open_access":"1"}],"scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"We compute the deficiency spaces of operators of the form 𝐻𝐴⊗̂ 𝐼+𝐼⊗̂ 𝐻𝐵, for symmetric 𝐻𝐴 and self-adjoint 𝐻𝐵. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301], but only proven under the restriction of 𝐻𝐵 having discrete, non-degenerate spectrum.","lang":"eng"}],"department":[{"_id":"JaMa"}],"date_updated":"2023-08-17T07:12:05Z","status":"public","article_type":"original","type":"journal_article","_id":"9627"},{"oa":1,"publisher":"Institute of Science and Technology Austria","acknowledgement":"The author gratefully acknowledges support by the Austrian Science Fund (FWF), grants No W1245.","date_created":"2021-09-21T09:14:15Z","doi":"10.15479/at:ista:10030","date_published":"2021-09-22T00:00:00Z","day":"22","year":"2021","has_accepted_license":"1","project":[{"call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"title":"Discrete-to-continuum limits of transport problems and gradient flows in the space of measures","article_processing_charge":"No","author":[{"first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","full_name":"Portinale, Lorenzo","last_name":"Portinale"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","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.","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","mla":"Portinale, Lorenzo. Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:10030.","ista":"Portinale L. 2021. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. Institute of Science and Technology Austria.","chicago":"Portinale, Lorenzo. “Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:10030."},"month":"09","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"NanoFab"}],"abstract":[{"lang":"eng","text":"This PhD thesis is primarily focused on the study of discrete transport problems, introduced for the first time in the seminal works of Maas [Maa11] and Mielke [Mie11] on finite state Markov chains and reaction-diffusion equations, respectively. More in detail, my research focuses on the study of transport costs on graphs, in particular the convergence and the stability of such problems in the discrete-to-continuum limit. This thesis also includes some results concerning\r\nnon-commutative optimal transport. The first chapter of this thesis consists of a general introduction to the optimal transport problems, both in the discrete, the continuous, and the non-commutative setting. Chapters 2 and 3 present the content of two works, obtained in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have been able to show the convergence of discrete transport costs on periodic graphs to suitable continuous ones, which can be described by means of a homogenisation result. We first focus on the particular case of quadratic costs on the real line and then extending the result to more general costs in arbitrary dimension. Our results are the first complete characterisation of limits of transport costs on periodic graphs in arbitrary dimension which do not rely on any additional symmetry. In Chapter 4 we turn our attention to one of the intriguing connection between evolution equations and optimal transport, represented by the theory of gradient flows. We show that discrete gradient flow structures associated to a finite volume approximation of a certain class of diffusive equations (Fokker–Planck) is stable in the limit of vanishing meshes, reproving the convergence of the scheme via the method of evolutionary Γ-convergence and exploiting a more variational point of view on the problem. This is based on a collaboration with Dominik Forkert and Jan Maas. Chapter 5 represents a change of perspective, moving away from the discrete world and reaching the non-commutative one. As in the discrete case, we discuss how classical tools coming from the commutative optimal transport can be translated into the setting of density matrices. In particular, in this final chapter we present a non-commutative version of the Schrödinger problem (or entropic regularised optimal transport problem) and discuss existence and characterisation of minimisers, a duality result, and present a non-commutative version of the well-known Sinkhorn algorithm to compute the above mentioned optimisers. This is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally, Appendix A and B contain some additional material and discussions, with particular attention to Harnack inequalities and the regularity of flows on discrete spaces."}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"10022"},{"relation":"part_of_dissertation","status":"public","id":"9792"},{"relation":"part_of_dissertation","id":"7573","status":"public"}]},"language":[{"iso":"eng"}],"file":[{"date_created":"2021-09-21T09:17:34Z","file_name":"tex_and_pictures.zip","date_updated":"2022-03-10T12:14:42Z","file_size":3876668,"creator":"cchlebak","file_id":"10032","checksum":"8cd60dcb8762e8f21867e21e8001e183","content_type":"application/x-zip-compressed","access_level":"closed","relation":"source_file"},{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","checksum":"9789e9d967c853c1503ec7f307170279","file_id":"10047","file_size":2532673,"date_updated":"2021-09-27T11:14:31Z","creator":"cchlebak","file_name":"thesis_portinale_Final (1).pdf","date_created":"2021-09-27T11:14:31Z"}],"degree_awarded":"PhD","publication_status":"published","publication_identifier":{"issn":["2663-337X"]},"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"dissertation","_id":"10030","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"file_date_updated":"2022-03-10T12:14:42Z","ddc":["515"],"date_updated":"2023-09-07T13:31:06Z","supervisor":[{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas"}]},{"oa":1,"acknowledgement":"This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thanks the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. Finally, the authors also thanks J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and NoF65. D.F acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942].","date_created":"2021-08-06T09:07:12Z","date_published":"2021-07-21T00:00:00Z","doi":"10.48550/arXiv.2106.11217","publication":"arXiv","day":"21","year":"2021","has_accepted_license":"1","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"article_number":"2106.11217","title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","article_processing_charge":"No","external_id":{"arxiv":["2106.11217"]},"author":[{"first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","last_name":"Feliciangeli","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario"},{"last_name":"Gerolin","full_name":"Gerolin, Augusto","first_name":"Augusto"},{"last_name":"Portinale","full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. 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. .","short":"D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.).","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","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","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."},"month":"07","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2106.11217","open_access":"1"}],"oa_version":"Preprint","abstract":[{"text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on careful a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.","lang":"eng"}],"ec_funded":1,"related_material":{"record":[{"id":"9733","status":"public","relation":"dissertation_contains"},{"status":"public","id":"10030","relation":"dissertation_contains"},{"relation":"later_version","status":"public","id":"12911"}]},"language":[{"iso":"eng"}],"publication_status":"submitted","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"preprint","_id":"9792","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"ddc":["510"],"date_updated":"2023-11-14T13:21:01Z"},{"file_date_updated":"2022-03-10T12:13:57Z","department":[{"_id":"GradSch"},{"_id":"RoSe"},{"_id":"JaMa"}],"date_updated":"2024-03-06T12:30:44Z","supervisor":[{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"ddc":["515","519","539"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","short":"CC BY-ND (4.0)"},"type":"dissertation","status":"public","_id":"9733","license":"https://creativecommons.org/licenses/by-nd/4.0/","ec_funded":1,"related_material":{"record":[{"relation":"part_of_dissertation","id":"9787","status":"public"},{"relation":"part_of_dissertation","id":"9792","status":"public"},{"status":"public","id":"9225","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"9781","status":"public"},{"id":"9791","status":"public","relation":"part_of_dissertation"}]},"degree_awarded":"PhD","publication_status":"published","publication_identifier":{"issn":["2663-337X"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"9944","checksum":"e88bb8ca43948abe060eb2d2fa719881","file_size":1958710,"date_updated":"2021-09-06T09:28:56Z","creator":"dfelicia","file_name":"Thesis_FeliciangeliA.pdf","date_created":"2021-08-19T14:03:48Z"},{"access_level":"closed","relation":"source_file","content_type":"application/octet-stream","checksum":"72810843abee83705853505b3f8348aa","file_id":"9945","creator":"dfelicia","date_updated":"2022-03-10T12:13:57Z","file_size":3771669,"date_created":"2021-08-19T14:06:35Z","file_name":"thesis.7z"}],"alternative_title":["ISTA Thesis"],"month":"08","abstract":[{"text":"This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author.","lang":"eng"}],"oa_version":"Published Version","article_processing_charge":"No","author":[{"full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario"}],"title":"The polaron at strong coupling","citation":{"ieee":"D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and Technology Austria, 2021.","short":"D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and Technology Austria, 2021.","apa":"Feliciangeli, D. (2021). The polaron at strong coupling. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:9733","ama":"Feliciangeli D. The polaron at strong coupling. 2021. doi:10.15479/at:ista:9733","mla":"Feliciangeli, Dario. The Polaron at Strong Coupling. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:9733.","ista":"Feliciangeli D. 2021. The polaron at strong coupling. 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Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. Journal of Statistical Physics. 178(2), 319–378.","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.","short":"E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378.","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.","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","ama":"Carlen EA, Maas J. 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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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 178","month":"01","date_updated":"2023-08-17T13:49:40Z","ddc":["500"],"department":[{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:47:28Z","_id":"6358","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public"},{"date_updated":"2023-08-17T13:48:31Z","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"_id":"74","series_title":"LNM","status":"public","type":"book_chapter","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"isbn":["9783030360191"],"eissn":["16179692"],"issn":["00758434"],"eisbn":["9783030360207"]},"ec_funded":1,"volume":2256,"oa_version":"Preprint","abstract":[{"text":"We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean space, motivated by the famous theorem of Gromov about the waist of radially symmetric Gaussian measures. In particular, it turns our possible to extend Gromov’s original result to the case of not necessarily radially symmetric Gaussian measure. We also provide examples of measures having no t-neighborhood waist property, including a rather wide class\r\nof compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument to produce some estimates of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures.","lang":"eng"}],"intvolume":" 2256","month":"06","main_file_link":[{"url":"https://arxiv.org/abs/1808.07350","open_access":"1"}],"scopus_import":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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","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","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.","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 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.","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.","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."},"editor":[{"first_name":"Bo'az","last_name":"Klartag","full_name":"Klartag, Bo'az"},{"last_name":"Milman","full_name":"Milman, Emanuel","first_name":"Emanuel"}],"title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","article_processing_charge":"No","external_id":{"arxiv":["1808.07350"],"isi":["000557689300003"]},"author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"publication":"Geometric Aspects of Functional Analysis","day":"21","year":"2020","isi":1,"date_created":"2018-12-11T11:44:29Z","date_published":"2020-06-21T00:00:00Z","doi":"10.1007/978-3-030-36020-7_1","page":"1-27","oa":1,"publisher":"Springer Nature","quality_controlled":"1"},{"date_updated":"2023-08-17T14:35:46Z","department":[{"_id":"JaMa"}],"_id":"7388","status":"public","type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0294-1449"]},"issue":"3","volume":37,"oa_version":"Preprint","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."}],"intvolume":" 37","month":"05","main_file_link":[{"url":"https://arxiv.org/abs/1902.07635","open_access":"1"}],"scopus_import":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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","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","short":"M. Gerencser, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 37 (2020) 663–682.","ieee":"M. Gerencser, “Nondivergence form quasilinear heat equations driven by space-time white noise,” Annales de l’Institut Henri Poincaré C, Analyse non linéaire, vol. 37, no. 3. Elsevier, pp. 663–682, 2020.","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.","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."},"title":"Nondivergence form quasilinear heat equations driven by space-time white noise","article_processing_charge":"No","external_id":{"arxiv":["1902.07635"],"isi":["000531049800007"]},"author":[{"full_name":"Gerencser, Mate","last_name":"Gerencser","first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87"}],"publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","day":"01","year":"2020","isi":1,"date_created":"2020-01-29T09:39:41Z","date_published":"2020-05-01T00:00:00Z","doi":"10.1016/j.anihpc.2020.01.003","page":"663-682","oa":1,"publisher":"Elsevier","quality_controlled":"1"},{"volume":365,"ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.01205"}],"month":"05","intvolume":" 365","abstract":[{"lang":"eng","text":"In this paper we study the joint convexity/concavity of the trace functions Ψp,q,s(A,B)=Tr(Bq2K∗ApKBq2)s, p,q,s∈R,\r\nwhere A and B are positive definite matrices and K is any fixed invertible matrix. We will give full range of (p,q,s)∈R3 for Ψp,q,s to be jointly convex/concave for all K. As a consequence, we confirm a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture of Audenaert and Datta and obtain the full range of (α,z) for α-z Rényi relative entropies to be monotone under completely positive trace preserving maps. We also give simpler proofs of many known results, including the concavity of Ψp,0,1/p for 0
Advances in Mathematics. Elsevier, 2020. https://doi.org/10.1016/j.aim.2020.107053.","ieee":"H. Zhang, “From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture,” Advances in Mathematics, vol. 365. Elsevier, 2020.","short":"H. Zhang, Advances in Mathematics 365 (2020).","ama":"Zhang H. From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics. 2020;365. doi:10.1016/j.aim.2020.107053","apa":"Zhang, H. (2020). From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2020.107053","mla":"Zhang, Haonan. “From Wigner-Yanase-Dyson Conjecture to Carlen-Frank-Lieb Conjecture.” Advances in Mathematics, vol. 365, 107053, Elsevier, 2020, doi:10.1016/j.aim.2020.107053."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"article_number":"107053"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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.","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","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","ieee":"H. Zhang, “Equality conditions of data processing inequality for α-z Rényi relative entropies,” Journal of Mathematical Physics, vol. 61, no. 10. AIP Publishing, 2020.","short":"H. Zhang, Journal of Mathematical Physics 61 (2020)."},"title":"Equality conditions of data processing inequality for α-z Rényi relative entropies","article_processing_charge":"No","external_id":{"arxiv":["2007.06644"],"isi":["000578529200001"]},"author":[{"last_name":"Zhang","full_name":"Zhang, Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan"}],"article_number":"102201","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"publication":"Journal of Mathematical Physics","day":"01","year":"2020","isi":1,"date_created":"2020-10-18T22:01:36Z","date_published":"2020-10-01T00:00:00Z","doi":"10.1063/5.0022787","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.","oa":1,"quality_controlled":"1","publisher":"AIP Publishing","date_updated":"2023-08-22T10:32:29Z","department":[{"_id":"JaMa"}],"_id":"8670","status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["00222488"]},"ec_funded":1,"volume":61,"issue":"10","oa_version":"Preprint","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)]."}],"intvolume":" 61","month":"10","main_file_link":[{"url":"https://arxiv.org/abs/2007.06644","open_access":"1"}],"scopus_import":"1"},{"page":"2257-2303","date_published":"2020-12-01T00:00:00Z","doi":"10.1007/s10955-020-02663-4","date_created":"2020-11-15T23:01:18Z","isi":1,"has_accepted_license":"1","year":"2020","day":"01","publication":"Journal of Statistical Physics","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"The research of A.M. was partially supported by the Deutsche Forschungsgemeinschaft (DFG) via the Collaborative Research Center SFB 1114 Scaling Cascades in Complex Systems (Project No. 235221301), through the Subproject C05 Effective models for materials and interfaces with multiple scales. J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117), and by the Austrian Science Fund (FWF), Project SFB F65. The authors thank Christof Schütte, Robert I. A. Patterson, and Stefanie Winkelmann for helpful and stimulating discussions. Open access funding provided by Austrian Science Fund (FWF).","author":[{"full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"},{"first_name":"Alexander","last_name":"Mielke","full_name":"Mielke, Alexander"}],"external_id":{"isi":["000587107200002"],"arxiv":["2004.02831"]},"article_processing_charge":"No","title":"Modeling of chemical reaction systems with detailed balance using gradient structures","citation":{"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.","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.","short":"J. Maas, A. Mielke, Journal of Statistical Physics 181 (2020) 2257–2303.","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425","name":"Taming Complexity in Partial Di erential Systems","grant_number":" F06504"}],"volume":181,"issue":"6","ec_funded":1,"publication_identifier":{"issn":["00224715"],"eissn":["15729613"]},"publication_status":"published","file":[{"success":1,"checksum":"bc2b63a90197b97cbc73eccada4639f5","file_id":"9087","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2020_JourStatPhysics_Maas.pdf","date_created":"2021-02-04T10:29:11Z","file_size":753596,"date_updated":"2021-02-04T10:29:11Z","creator":"dernst"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"12","intvolume":" 181","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."}],"oa_version":"Published Version","department":[{"_id":"JaMa"}],"file_date_updated":"2021-02-04T10:29:11Z","date_updated":"2023-08-22T13:24:27Z","ddc":["510"],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"8758"},{"oa_version":"Published Version","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."}],"month":"03","alternative_title":["ISTA Thesis"],"language":[{"iso":"eng"}],"file":[{"file_id":"7657","checksum":"c814a1a6195269ca6fe48b0dca45ae8a","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2020-04-14T10:47:59Z","file_name":"Thesis_Forkert_PDFA.pdf","date_updated":"2020-07-14T12:48:01Z","file_size":3297129,"creator":"dernst"},{"creator":"dernst","date_updated":"2020-07-14T12:48:01Z","file_size":1063908,"date_created":"2020-04-14T10:47:59Z","file_name":"Thesis_Forkert_source.zip","access_level":"closed","relation":"source_file","content_type":"application/x-zip-compressed","file_id":"7658","checksum":"ceafb53f923d1b5bdf14b2b0f22e4a81"}],"publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"ec_funded":1,"_id":"7629","status":"public","type":"dissertation","ddc":["510"],"date_updated":"2023-09-07T13:03:12Z","supervisor":[{"full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"department":[{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:48:01Z","oa":1,"publisher":"Institute of Science and Technology Austria","day":"31","year":"2020","has_accepted_license":"1","date_created":"2020-04-02T06:40:23Z","date_published":"2020-03-31T00:00:00Z","doi":"10.15479/AT:ISTA:7629","page":"154","project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Forkert, Dominik L. “Gradient Flows in Spaces of Probability Measures for Finite-Volume Schemes, Metric Graphs and Non-Reversible Markov Chains.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7629.","ista":"Forkert DL. 2020. Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains. Institute of Science and Technology Austria.","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.","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","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.","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."},"title":"Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains","article_processing_charge":"No","author":[{"first_name":"Dominik L","id":"35C79D68-F248-11E8-B48F-1D18A9856A87","last_name":"Forkert","full_name":"Forkert, Dominik L"}]},{"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Di erential Systems","grant_number":" F06504","call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations"}],"citation":{"short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Journal de Mathematiques Pures et Appliquees 139 (2020) 204–234.","ieee":"P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of one-dimensional discrete optimal transport,” Journal de Mathematiques Pures et Appliquees, vol. 139, no. 7. Elsevier, pp. 204–234, 2020.","apa":"Gladbach, P., Kopfer, E., Maas, J., & Portinale, L. (2020). Homogenisation of one-dimensional discrete optimal transport. Journal de Mathematiques Pures et Appliquees. Elsevier. https://doi.org/10.1016/j.matpur.2020.02.008","ama":"Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of one-dimensional discrete optimal transport. Journal de Mathematiques Pures et Appliquees. 2020;139(7):204-234. doi:10.1016/j.matpur.2020.02.008","mla":"Gladbach, Peter, et al. “Homogenisation of One-Dimensional Discrete Optimal Transport.” Journal de Mathematiques Pures et Appliquees, vol. 139, no. 7, Elsevier, 2020, pp. 204–34, doi:10.1016/j.matpur.2020.02.008.","ista":"Gladbach P, Kopfer E, Maas J, Portinale L. 2020. Homogenisation of one-dimensional discrete optimal transport. Journal de Mathematiques Pures et Appliquees. 139(7), 204–234.","chicago":"Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of One-Dimensional Discrete Optimal Transport.” Journal de Mathematiques Pures et Appliquees. Elsevier, 2020. https://doi.org/10.1016/j.matpur.2020.02.008."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Gladbach, Peter","last_name":"Gladbach","first_name":"Peter"},{"last_name":"Kopfer","full_name":"Kopfer, Eva","first_name":"Eva"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan"},{"first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale","full_name":"Portinale, Lorenzo"}],"external_id":{"arxiv":["1905.05757"],"isi":["000539439400008"]},"article_processing_charge":"No","title":"Homogenisation of one-dimensional discrete optimal transport","acknowledgement":"J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 716117). J.M. and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 350398276.","quality_controlled":"1","publisher":"Elsevier","oa":1,"isi":1,"year":"2020","day":"01","publication":"Journal de Mathematiques Pures et Appliquees","page":"204-234","doi":"10.1016/j.matpur.2020.02.008","date_published":"2020-07-01T00:00:00Z","date_created":"2020-03-08T23:00:47Z","_id":"7573","article_type":"original","type":"journal_article","status":"public","date_updated":"2023-09-07T13:31:05Z","department":[{"_id":"JaMa"}],"abstract":[{"text":"This paper deals with dynamical optimal transport metrics defined by spatial discretisation of the Benamou–Benamou formula for the Kantorovich metric . Such metrics appear naturally in discretisations of -gradient flow formulations for dissipative PDE. However, it has recently been shown that these metrics do not in general converge to , unless strong geometric constraints are imposed on the discrete mesh. In this paper we prove that, in a 1-dimensional periodic setting, discrete transport metrics converge to a limiting transport metric with a non-trivial effective mobility. This mobility depends sensitively on the geometry of the mesh and on the non-local mobility at the discrete level. Our result quantifies to what extent discrete transport can make use of microstructure in the mesh to reduce the cost of transport.","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1905.05757"}],"month":"07","intvolume":" 139","publication_identifier":{"issn":["00217824"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":139,"related_material":{"record":[{"status":"public","id":"10030","relation":"dissertation_contains"}]},"issue":"7","ec_funded":1},{"_id":"10022","article_number":"2008.10962","type":"preprint","project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"status":"public","citation":{"mla":"Forkert, Dominik L., et al. “Evolutionary Γ-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” ArXiv, 2008.10962.","ama":"Forkert DL, Maas J, Portinale L. Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. arXiv.","apa":"Forkert, D. L., Maas, J., & Portinale, L. (n.d.). Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. arXiv.","short":"D.L. Forkert, J. Maas, L. Portinale, ArXiv (n.d.).","ieee":"D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” arXiv. .","chicago":"Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary Γ-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” ArXiv, n.d.","ista":"Forkert DL, Maas J, Portinale L. Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. arXiv, 2008.10962."},"date_updated":"2023-09-07T13:31:05Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","article_processing_charge":"No","external_id":{"arxiv":["2008.10962"]},"author":[{"full_name":"Forkert, Dominik L","last_name":"Forkert","id":"35C79D68-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik L"},{"last_name":"Maas","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Portinale","full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo"}],"title":"Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions","department":[{"_id":"JaMa"}],"abstract":[{"lang":"eng","text":"We consider finite-volume approximations of Fokker-Planck equations on bounded convex domains in R^d and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker-Planck equation via the method of Evolutionary Γ-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalising the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality."}],"acknowledgement":"This work is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117) and by the Austrian Science Fund (FWF), grants No F65 and W1245.","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2008.10962"}],"oa":1,"month":"08","publication_status":"submitted","year":"2020","publication":"arXiv","language":[{"iso":"eng"}],"day":"25","page":"33","date_created":"2021-09-17T10:57:27Z","ec_funded":1,"date_published":"2020-08-25T00:00:00Z","related_material":{"record":[{"relation":"later_version","id":"11739","status":"public"},{"relation":"dissertation_contains","status":"public","id":"10030"}]}},{"article_type":"original","type":"journal_article","status":"public","_id":"71","department":[{"_id":"JaMa"}],"date_updated":"2023-09-18T08:13:15Z","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1809.01092"}],"month":"10","intvolume":" 52","abstract":[{"text":"We consider dynamical transport metrics for probability measures on discretisations of a bounded convex domain in ℝd. These metrics are natural discrete counterparts to the Kantorovich metric 𝕎2, defined using a Benamou-Brenier type formula. Under mild assumptions we prove an asymptotic upper bound for the discrete transport metric Wt in terms of 𝕎2, as the size of the mesh T tends to 0. However, we show that the corresponding lower bound may fail in general, even on certain one-dimensional and symmetric two-dimensional meshes. In addition, we show that the asymptotic lower bound holds under an isotropy assumption on the mesh, which turns out to be essentially necessary. This assumption is satisfied, e.g., for tilings by convex regular polygons, and it implies Gromov-Hausdorff convergence of the transport metric.","lang":"eng"}],"oa_version":"Preprint","issue":"3","volume":52,"publication_identifier":{"eissn":["10957154"],"issn":["00361410"]},"publication_status":"published","language":[{"iso":"eng"}],"publist_id":"7983","author":[{"first_name":"Peter","last_name":"Gladbach","full_name":"Gladbach, Peter"},{"full_name":"Kopfer, Eva","last_name":"Kopfer","first_name":"Eva"},{"first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas"}],"article_processing_charge":"No","external_id":{"isi":["000546975100017"],"arxiv":["1809.01092"]},"title":"Scaling limits of discrete optimal transport","citation":{"ista":"Gladbach P, Kopfer E, Maas J. 2020. Scaling limits of discrete optimal transport. SIAM Journal on Mathematical Analysis. 52(3), 2759–2802.","chicago":"Gladbach, Peter, Eva Kopfer, and Jan Maas. “Scaling Limits of Discrete Optimal Transport.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2020. https://doi.org/10.1137/19M1243440.","short":"P. Gladbach, E. Kopfer, J. Maas, SIAM Journal on Mathematical Analysis 52 (2020) 2759–2802.","ieee":"P. Gladbach, E. Kopfer, and J. Maas, “Scaling limits of discrete optimal transport,” SIAM Journal on Mathematical Analysis, vol. 52, no. 3. Society for Industrial and Applied Mathematics, pp. 2759–2802, 2020.","ama":"Gladbach P, Kopfer E, Maas J. Scaling limits of discrete optimal transport. SIAM Journal on Mathematical Analysis. 2020;52(3):2759-2802. doi:10.1137/19M1243440","apa":"Gladbach, P., Kopfer, E., & Maas, J. (2020). Scaling limits of discrete optimal transport. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1243440","mla":"Gladbach, Peter, et al. “Scaling Limits of Discrete Optimal Transport.” SIAM Journal on Mathematical Analysis, vol. 52, no. 3, Society for Industrial and Applied Mathematics, 2020, pp. 2759–802, doi:10.1137/19M1243440."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics","oa":1,"page":"2759-2802","date_published":"2020-10-01T00:00:00Z","doi":"10.1137/19M1243440","date_created":"2018-12-11T11:44:28Z","isi":1,"year":"2020","day":"01","publication":"SIAM Journal on Mathematical Analysis"},{"citation":{"short":"K. Dareiotis, M. Gerencser, Electronic Journal of Probability 25 (2020).","ieee":"K. Dareiotis and M. Gerencser, “On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift,” Electronic Journal of Probability, vol. 25. Institute of Mathematical Statistics, 2020.","apa":"Dareiotis, K., & Gerencser, M. (2020). On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/20-EJP479","ama":"Dareiotis K, Gerencser M. On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. 2020;25. doi:10.1214/20-EJP479","mla":"Dareiotis, Konstantinos, and Mate Gerencser. “On the Regularisation of the Noise for the Euler-Maruyama Scheme with Irregular Drift.” Electronic Journal of Probability, vol. 25, 82, Institute of Mathematical Statistics, 2020, doi:10.1214/20-EJP479.","ista":"Dareiotis K, Gerencser M. 2020. On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. 25, 82.","chicago":"Dareiotis, Konstantinos, and Mate Gerencser. “On the Regularisation of the Noise for the Euler-Maruyama Scheme with Irregular Drift.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/20-EJP479."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Konstantinos","full_name":"Dareiotis, Konstantinos","last_name":"Dareiotis"},{"id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87","first_name":"Mate","full_name":"Gerencser, Mate","last_name":"Gerencser"}],"external_id":{"arxiv":["1812.04583"],"isi":["000550150700001"]},"article_processing_charge":"No","title":"On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift","article_number":"82","has_accepted_license":"1","isi":1,"year":"2020","day":"16","publication":"Electronic Journal of Probability","doi":"10.1214/20-EJP479","date_published":"2020-07-16T00:00:00Z","date_created":"2019-04-30T07:40:17Z","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"date_updated":"2023-10-16T09:22:50Z","ddc":["510"],"file_date_updated":"2020-09-21T13:15:02Z","department":[{"_id":"JaMa"}],"_id":"6359","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","publication_identifier":{"eissn":["1083-6489"]},"publication_status":"published","file":[{"date_updated":"2020-09-21T13:15:02Z","file_size":273042,"creator":"dernst","date_created":"2020-09-21T13:15:02Z","file_name":"2020_EJournProbab_Dareiotis.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"8549","checksum":"8e7c42e72596f6889d786e8e8b89994f","success":1}],"language":[{"iso":"eng"}],"volume":25,"abstract":[{"lang":"eng","text":"The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of α-Hölder drift in the recent literature the rate α/2 was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to 1/2 for all α>0. The result extends to Dini continuous coefficients, while in d=1 also to all bounded measurable coefficients."}],"oa_version":"Published Version","scopus_import":"1","month":"07","intvolume":" 25"},{"acknowledgement":"We warmly thank S.R.S. Varadhan for many enlightening discussions at an early stage of this work. We are indebted to Francesca Collet for fruitful discussions and constant support all throughout this work. We thank Simone Floreani\r\nand Alberto Chiarini for helpful conversations on the final part of this paper as well as both referees for their careful reading and for raising relevant issues on some weak points contained in a previous version of this manuscript; we believe this helped us to improve it.\r\nPart of this work was done during the authors’ stay at the Institut Henri Poincaré (UMS 5208 CNRS-Sorbonne Université) – Centre Emile Borel during the trimester Stochastic Dynamics Out of Equilibrium. The authors thank this institution for hospitality and support (through LabEx CARMIN, ANR-10-LABX-59-01). F.S. thanks laboratoire\r\nMAP5 of Université de Paris, and E.S. thanks Delft University, for financial support and hospitality. F.S. acknowledges NWO for financial support via the TOP1 grant 613.001.552 as well as funding from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411. This research has been conducted within the FP2M federation (CNRS FR 2036).","publisher":" Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"day":"21","publication":"Electronic Journal of Probability","has_accepted_license":"1","isi":1,"year":"2020","doi":"10.1214/20-EJP536","date_published":"2020-10-21T00:00:00Z","date_created":"2020-12-27T23:01:17Z","article_number":"138","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Redig, F., Saada, E., & Sau, F. (2020). Symmetric simple exclusion process in dynamic environment: Hydrodynamics. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/20-EJP536","ama":"Redig F, Saada E, Sau F. Symmetric simple exclusion process in dynamic environment: Hydrodynamics. Electronic Journal of Probability. 2020;25. doi:10.1214/20-EJP536","short":"F. Redig, E. Saada, F. Sau, Electronic Journal of Probability 25 (2020).","ieee":"F. Redig, E. Saada, and F. Sau, “Symmetric simple exclusion process in dynamic environment: Hydrodynamics,” Electronic Journal of Probability, vol. 25. Institute of Mathematical Statistics, 2020.","mla":"Redig, Frank, et al. “Symmetric Simple Exclusion Process in Dynamic Environment: Hydrodynamics.” Electronic Journal of Probability, vol. 25, 138, Institute of Mathematical Statistics, 2020, doi:10.1214/20-EJP536.","ista":"Redig F, Saada E, Sau F. 2020. Symmetric simple exclusion process in dynamic environment: Hydrodynamics. Electronic Journal of Probability. 25, 138.","chicago":"Redig, Frank, Ellen Saada, and Federico Sau. “Symmetric Simple Exclusion Process in Dynamic Environment: Hydrodynamics.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/20-EJP536."},"title":"Symmetric simple exclusion process in dynamic environment: Hydrodynamics","author":[{"first_name":"Frank","full_name":"Redig, Frank","last_name":"Redig"},{"full_name":"Saada, Ellen","last_name":"Saada","first_name":"Ellen"},{"first_name":"Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425","last_name":"Sau","full_name":"Sau, Federico"}],"external_id":{"arxiv":["1811.01366"],"isi":["000591737500001"]},"article_processing_charge":"No","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider the symmetric simple exclusion process in Zd with quenched bounded dynamic random conductances and prove its hydrodynamic limit in path space. The main tool is the connection, due to the self-duality of the process, between the invariance principle for single particles starting from all points and the macroscopic behavior of the density field. While the hydrodynamic limit at fixed macroscopic times is obtained via a generalization to the time-inhomogeneous context of the strategy introduced in [41], in order to prove tightness for the sequence of empirical density fields we develop a new criterion based on the notion of uniform conditional stochastic continuity, following [50]. In conclusion, we show that uniform elliptic dynamic conductances provide an example of environments in which the so-called arbitrary starting point invariance principle may be derived from the invariance principle of a single particle starting from the origin. Therefore, our hydrodynamics result applies to the examples of quenched environments considered in, e.g., [1], [3], [6] in combination with the hypothesis of uniform ellipticity."}],"month":"10","intvolume":" 25","scopus_import":"1","file":[{"success":1,"file_id":"8976","checksum":"d75359b9814e78d57c0a481b7cde3751","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2020_ElectronJProbab_Redig.pdf","date_created":"2020-12-28T08:24:08Z","file_size":696653,"date_updated":"2020-12-28T08:24:08Z","creator":"dernst"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1083-6489"]},"publication_status":"published","volume":25,"ec_funded":1,"_id":"8973","status":"public","type":"journal_article","article_type":"original","ddc":["510"],"date_updated":"2023-10-17T12:51:56Z","department":[{"_id":"JaMa"}],"file_date_updated":"2020-12-28T08:24:08Z"},{"quality_controlled":"1","publisher":"Gakko Tosho","oa":1,"acknowledgement":"This work is supported by Vienna Science and Technology Fund (WWTF) through Project MA14-009 and by the Austrian Science Fund (FWF) projects F 65 and I 2375.","page":"425-447","date_published":"2019-10-22T00:00:00Z","date_created":"2020-02-28T10:54:41Z","year":"2019","day":"22","publication":"Advances in Mathematical Sciences and Applications","project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"author":[{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo","full_name":"Portinale, Lorenzo","last_name":"Portinale"},{"first_name":"Ulisse","full_name":"Stefanelli, Ulisse","last_name":"Stefanelli"}],"article_processing_charge":"No","external_id":{"arxiv":["1910.10050"]},"title":"Penalization via global functionals of optimal-control problems for dissipative evolution","citation":{"apa":"Portinale, L., & Stefanelli, U. (2019). Penalization via global functionals of optimal-control problems for dissipative evolution. Advances in Mathematical Sciences and Applications. Gakko Tosho.","ama":"Portinale L, Stefanelli U. Penalization via global functionals of optimal-control problems for dissipative evolution. Advances in Mathematical Sciences and Applications. 2019;28(2):425-447.","short":"L. Portinale, U. Stefanelli, Advances in Mathematical Sciences and Applications 28 (2019) 425–447.","ieee":"L. Portinale and U. Stefanelli, “Penalization via global functionals of optimal-control problems for dissipative evolution,” Advances in Mathematical Sciences and Applications, vol. 28, no. 2. Gakko Tosho, pp. 425–447, 2019.","mla":"Portinale, Lorenzo, and Ulisse Stefanelli. “Penalization via Global Functionals of Optimal-Control Problems for Dissipative Evolution.” Advances in Mathematical Sciences and Applications, vol. 28, no. 2, Gakko Tosho, 2019, pp. 425–47.","ista":"Portinale L, Stefanelli U. 2019. Penalization via global functionals of optimal-control problems for dissipative evolution. Advances in Mathematical Sciences and Applications. 28(2), 425–447.","chicago":"Portinale, Lorenzo, and Ulisse Stefanelli. “Penalization via Global Functionals of Optimal-Control Problems for Dissipative Evolution.” Advances in Mathematical Sciences and Applications. Gakko Tosho, 2019."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1910.10050","open_access":"1"}],"month":"10","intvolume":" 28","abstract":[{"lang":"eng","text":"We consider an optimal control problem for an abstract nonlinear dissipative evolution equation. The differential constraint is penalized by augmenting the target functional by a nonnegative global-in-time functional which is null-minimized in the evolution equation is satisfied. Different variational settings are presented, leading to the convergence of the penalization method for gradient flows, noncyclic and semimonotone flows, doubly nonlinear evolutions, and GENERIC systems. "}],"oa_version":"Preprint","issue":"2","volume":28,"publication_identifier":{"issn":["1343-4373"]},"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","article_type":"original","status":"public","_id":"7550","department":[{"_id":"JaMa"}],"date_updated":"2022-06-17T07:52:41Z"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ieee":"M. Gerencser and I. Gyöngy, “A Feynman–Kac formula for stochastic Dirichlet problems,” Stochastic Processes and their Applications, vol. 129, no. 3. Elsevier, pp. 995–1012, 2019.","short":"M. Gerencser, I. Gyöngy, Stochastic Processes and Their Applications 129 (2019) 995–1012.","apa":"Gerencser, M., & Gyöngy, I. (2019). A Feynman–Kac formula for stochastic Dirichlet problems. Stochastic Processes and Their Applications. Elsevier. https://doi.org/10.1016/j.spa.2018.04.003","ama":"Gerencser M, Gyöngy I. A Feynman–Kac formula for stochastic Dirichlet problems. Stochastic Processes and their Applications. 2019;129(3):995-1012. doi:10.1016/j.spa.2018.04.003","mla":"Gerencser, Mate, and István Gyöngy. “A Feynman–Kac Formula for Stochastic Dirichlet Problems.” Stochastic Processes and Their Applications, vol. 129, no. 3, Elsevier, 2019, pp. 995–1012, doi:10.1016/j.spa.2018.04.003.","ista":"Gerencser M, Gyöngy I. 2019. A Feynman–Kac formula for stochastic Dirichlet problems. Stochastic Processes and their Applications. 129(3), 995–1012.","chicago":"Gerencser, Mate, and István Gyöngy. “A Feynman–Kac Formula for Stochastic Dirichlet Problems.” Stochastic Processes and Their Applications. Elsevier, 2019. https://doi.org/10.1016/j.spa.2018.04.003."},"title":"A Feynman–Kac formula for stochastic Dirichlet problems","article_processing_charge":"No","external_id":{"isi":["000458945300012"],"arxiv":["1611.04177"]},"author":[{"first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87","full_name":"Gerencser, Mate","last_name":"Gerencser"},{"last_name":"Gyöngy","full_name":"Gyöngy, István","first_name":"István"}],"publication":"Stochastic Processes and their Applications","day":"01","year":"2019","isi":1,"date_created":"2018-12-11T11:45:42Z","doi":"10.1016/j.spa.2018.04.003","date_published":"2019-03-01T00:00:00Z","page":"995-1012","oa":1,"quality_controlled":"1","publisher":"Elsevier","date_updated":"2023-08-24T14:20:49Z","department":[{"_id":"JaMa"}],"_id":"301","status":"public","type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"publication_status":"published","issue":"3","volume":129,"oa_version":"Preprint","abstract":[{"lang":"eng","text":"A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that appear in the usual formulation are not even defined in the Itô sense."}],"intvolume":" 129","month":"03","main_file_link":[{"url":"https://arxiv.org/abs/1611.04177","open_access":"1"}],"scopus_import":"1"},{"citation":{"mla":"Dareiotis, Konstantinos, et al. “Entropy Solutions for Stochastic Porous Media Equations.” Journal of Differential Equations, vol. 266, no. 6, Elsevier, 2019, pp. 3732–63, doi:10.1016/j.jde.2018.09.012.","short":"K. Dareiotis, M. Gerencser, B. Gess, Journal of Differential Equations 266 (2019) 3732–3763.","ieee":"K. Dareiotis, M. Gerencser, and B. Gess, “Entropy solutions for stochastic porous media equations,” Journal of Differential Equations, vol. 266, no. 6. Elsevier, pp. 3732–3763, 2019.","apa":"Dareiotis, K., Gerencser, M., & Gess, B. (2019). Entropy solutions for stochastic porous media equations. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2018.09.012","ama":"Dareiotis K, Gerencser M, Gess B. Entropy solutions for stochastic porous media equations. Journal of Differential Equations. 2019;266(6):3732-3763. doi:10.1016/j.jde.2018.09.012","chicago":"Dareiotis, Konstantinos, Mate Gerencser, and Benjamin Gess. “Entropy Solutions for Stochastic Porous Media Equations.” Journal of Differential Equations. Elsevier, 2019. https://doi.org/10.1016/j.jde.2018.09.012.","ista":"Dareiotis K, Gerencser M, Gess B. 2019. Entropy solutions for stochastic porous media equations. Journal of Differential Equations. 266(6), 3732–3763."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000456332500026"],"arxiv":["1803.06953"]},"author":[{"first_name":"Konstantinos","last_name":"Dareiotis","full_name":"Dareiotis, Konstantinos"},{"first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87","full_name":"Gerencser, Mate","last_name":"Gerencser"},{"last_name":"Gess","full_name":"Gess, Benjamin","first_name":"Benjamin"}],"publist_id":"7989","title":"Entropy solutions for stochastic porous media equations","oa":1,"quality_controlled":"1","publisher":"Elsevier","year":"2019","isi":1,"publication":"Journal of Differential Equations","day":"5","page":"3732-3763","date_created":"2018-12-11T11:44:26Z","date_published":"2019-03-05T00:00:00Z","doi":"10.1016/j.jde.2018.09.012","_id":"65","type":"journal_article","article_type":"original","status":"public","date_updated":"2023-08-24T14:30:16Z","department":[{"_id":"JaMa"}],"abstract":[{"lang":"eng","text":"We provide an entropy formulation for porous medium-type equations with a stochastic, non-linear, spatially inhomogeneous forcing. Well-posedness and L1-contraction is obtained in the class of entropy solutions. Our scope allows for porous medium operators Δ(|u|m−1u) for all m∈(1,∞), and Hölder continuous diffusion nonlinearity with exponent 1/2."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1803.06953"}],"scopus_import":"1","intvolume":" 266","month":"03","publication_status":"published","language":[{"iso":"eng"}],"volume":266,"issue":"6"},{"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"author":[{"full_name":"Gerencser, Mate","last_name":"Gerencser","first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Martin","last_name":"Hairer","full_name":"Hairer, Martin"}],"publist_id":"7546","external_id":{"isi":["000463613800001"]},"article_processing_charge":"Yes (via OA deal)","title":"Singular SPDEs in domains with boundaries","citation":{"chicago":"Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.” Probability Theory and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0841-1.","ista":"Gerencser M, Hairer M. 2019. Singular SPDEs in domains with boundaries. Probability Theory and Related Fields. 173(3–4), 697–758.","mla":"Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.” Probability Theory and Related Fields, vol. 173, no. 3–4, Springer, 2019, pp. 697–758, doi:10.1007/s00440-018-0841-1.","apa":"Gerencser, M., & Hairer, M. (2019). Singular SPDEs in domains with boundaries. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-018-0841-1","ama":"Gerencser M, Hairer M. Singular SPDEs in domains with boundaries. Probability Theory and Related Fields. 2019;173(3-4):697–758. doi:10.1007/s00440-018-0841-1","short":"M. Gerencser, M. Hairer, Probability Theory and Related Fields 173 (2019) 697–758.","ieee":"M. Gerencser and M. Hairer, “Singular SPDEs in domains with boundaries,” Probability Theory and Related Fields, vol. 173, no. 3–4. Springer, pp. 697–758, 2019."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","publisher":"Springer","oa":1,"acknowledgement":"MG thanks the support of the LMS Postdoctoral Mobility Grant.\r\n\r\n","page":"697–758","date_published":"2019-04-01T00:00:00Z","doi":"10.1007/s00440-018-0841-1","date_created":"2018-12-11T11:45:48Z","has_accepted_license":"1","isi":1,"year":"2019","day":"01","publication":"Probability Theory and Related Fields","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"319","department":[{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:46:03Z","date_updated":"2023-08-24T14:38:32Z","ddc":["510"],"scopus_import":"1","month":"04","intvolume":" 173","abstract":[{"lang":"eng","text":"We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with boundary conditions. The calculus of modelled distributions established in Hairer (Invent Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4) is extended to this setting. We formulate and solve fixed point problems in these spaces with a class of kernels that is sufficiently large to cover in particular the Dirichlet and Neumann heat kernels. These results are then used to provide solution theories for the KPZ equation with Dirichlet and Neumann boundary conditions and for the 2D generalised parabolic Anderson model with Dirichlet boundary conditions. In the case of the KPZ equation with Neumann boundary conditions, we show that, depending on the class of mollifiers one considers, a “boundary renormalisation” takes place. In other words, there are situations in which a certain boundary condition is applied to an approximation to the KPZ equation, but the limiting process is the Hopf–Cole solution to the KPZ equation with a different boundary condition."}],"oa_version":"Published Version","issue":"3-4","volume":173,"publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"publication_status":"published","file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"288d16ef7291242f485a9660979486e3","file_id":"5722","creator":"dernst","date_updated":"2020-07-14T12:46:03Z","file_size":893182,"date_created":"2018-12-17T16:25:24Z","file_name":"2018_ProbTheory_Gerencser.pdf"}],"language":[{"iso":"eng"}]},{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","status":"public","_id":"6028","file_date_updated":"2020-07-14T12:47:17Z","department":[{"_id":"JaMa"}],"date_updated":"2023-08-24T14:44:31Z","ddc":["500"],"scopus_import":"1","intvolume":" 72","month":"02","abstract":[{"lang":"eng","text":"We give a construction allowing us to build local renormalized solutions to general quasilinear stochastic PDEs within the theory of regularity structures, thus greatly generalizing the recent results of [1, 5, 11]. Loosely speaking, our construction covers quasilinear variants of all classes of equations for which the general construction of [3, 4, 7] applies, including in particular one‐dimensional systems with KPZ‐type nonlinearities driven by space‐time white noise. In a less singular and more specific case, we furthermore show that the counterterms introduced by the renormalization procedure are given by local functionals of the solution. The main feature of our construction is that it allows exploitation of a number of existing results developed for the semilinear case, so that the number of additional arguments it requires is relatively small."}],"oa_version":"Published Version","issue":"9","volume":72,"publication_status":"published","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"7237","checksum":"09aec427eb48c0f96a1cce9ff53f013b","file_size":381350,"date_updated":"2020-07-14T12:47:17Z","creator":"kschuh","file_name":"2019_Wiley_Gerencser.pdf","date_created":"2020-01-07T13:25:55Z"}],"external_id":{"isi":["000475465000003"]},"article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Gerencser, Mate","last_name":"Gerencser","first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Martin","last_name":"Hairer","full_name":"Hairer, Martin"}],"title":"A solution theory for quasilinear singular SPDEs","citation":{"ista":"Gerencser M, Hairer M. 2019. A solution theory for quasilinear singular SPDEs. Communications on Pure and Applied Mathematics. 72(9), 1983–2005.","chicago":"Gerencser, Mate, and Martin Hairer. “A Solution Theory for Quasilinear Singular SPDEs.” Communications on Pure and Applied Mathematics. Wiley, 2019. https://doi.org/10.1002/cpa.21816.","short":"M. Gerencser, M. Hairer, Communications on Pure and Applied Mathematics 72 (2019) 1983–2005.","ieee":"M. Gerencser and M. Hairer, “A solution theory for quasilinear singular SPDEs,” Communications on Pure and Applied Mathematics, vol. 72, no. 9. Wiley, pp. 1983–2005, 2019.","ama":"Gerencser M, Hairer M. A solution theory for quasilinear singular SPDEs. Communications on Pure and Applied Mathematics. 2019;72(9):1983-2005. doi:10.1002/cpa.21816","apa":"Gerencser, M., & Hairer, M. (2019). A solution theory for quasilinear singular SPDEs. Communications on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.21816","mla":"Gerencser, Mate, and Martin Hairer. “A Solution Theory for Quasilinear Singular SPDEs.” Communications on Pure and Applied Mathematics, vol. 72, no. 9, Wiley, 2019, pp. 1983–2005, doi:10.1002/cpa.21816."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"quality_controlled":"1","publisher":"Wiley","page":"1983-2005","date_created":"2019-02-17T22:59:24Z","date_published":"2019-02-08T00:00:00Z","doi":"10.1002/cpa.21816","year":"2019","has_accepted_license":"1","isi":1,"publication":"Communications on Pure and Applied Mathematics","day":"08"},{"title":"Boundary regularity of stochastic PDEs","external_id":{"isi":["000459681900005"],"arxiv":["1705.05364"]},"article_processing_charge":"No","author":[{"last_name":"Gerencser","full_name":"Gerencser, Mate","first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Gerencser, Mate. “Boundary Regularity of Stochastic PDEs.” Annals of Probability. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AOP1272.","ista":"Gerencser M. 2019. Boundary regularity of stochastic PDEs. Annals of Probability. 47(2), 804–834.","mla":"Gerencser, Mate. “Boundary Regularity of Stochastic PDEs.” Annals of Probability, vol. 47, no. 2, Institute of Mathematical Statistics, 2019, pp. 804–34, doi:10.1214/18-AOP1272.","apa":"Gerencser, M. (2019). Boundary regularity of stochastic PDEs. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AOP1272","ama":"Gerencser M. Boundary regularity of stochastic PDEs. Annals of Probability. 2019;47(2):804-834. doi:10.1214/18-AOP1272","short":"M. Gerencser, Annals of Probability 47 (2019) 804–834.","ieee":"M. Gerencser, “Boundary regularity of stochastic PDEs,” Annals of Probability, vol. 47, no. 2. Institute of Mathematical Statistics, pp. 804–834, 2019."},"date_created":"2019-04-07T21:59:15Z","doi":"10.1214/18-AOP1272","date_published":"2019-03-01T00:00:00Z","page":"804-834","publication":"Annals of Probability","day":"01","year":"2019","isi":1,"oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","department":[{"_id":"JaMa"}],"date_updated":"2023-08-25T08:59:11Z","status":"public","type":"journal_article","_id":"6232","volume":47,"issue":"2","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["00911798"]},"intvolume":" 47","month":"03","main_file_link":[{"url":"https://arxiv.org/abs/1705.05364","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"text":"The boundary behaviour of solutions of stochastic PDEs with Dirichlet boundary conditions can be surprisingly—and in a sense, arbitrarily—bad: as shown by Krylov[ SIAM J. Math. Anal.34(2003) 1167–1182], for any α>0 one can find a simple 1-dimensional constant coefficient linear equation whose solution at the boundary is not α-Hölder continuous.We obtain a positive counterpart of this: under some mild regularity assumptions on the coefficients, solutions of semilinear SPDEs on C1 domains are proved to be α-Hölder continuous up to the boundary with some α>0.","lang":"eng"}]},{"volume":39,"issue":"6","publication_identifier":{"issn":["1553-5231"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.04156"}],"month":"06","intvolume":" 39","abstract":[{"text":"Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with discontinuous coefficients for the action potential of each neuron and takes into account the (random) spatial configuration of neurons allowing the interaction to depend on it. In the limit as the number of particles tends to infinity, we obtain a nonlinear Fokker-Planck type PDE in two variables, with derivatives only with respect to one variable and discontinuous coefficients. We also study strong well-posedness of the system of SDEs and prove the existence and uniqueness of a weak measure-valued solution to the PDE, obtained as the limit of the laws of the empirical measures for the system of particles.","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"JaMa"}],"date_updated":"2023-09-08T11:34:45Z","article_type":"original","type":"journal_article","status":"public","keyword":["Applied Mathematics","Discrete Mathematics and Combinatorics","Analysis"],"_id":"10878","page":"3037-3067","date_published":"2019-06-01T00:00:00Z","doi":"10.3934/dcds.2019126","date_created":"2022-03-18T12:33:34Z","isi":1,"year":"2019","day":"01","publication":"Discrete and Continuous Dynamical Systems","quality_controlled":"1","publisher":"American Institute of Mathematical Sciences","oa":1,"acknowledgement":"The second author has been partially supported by INdAM through the GNAMPA Research\r\nProject (2017) “Sistemi stocastici singolari: buona posizione e problemi di controllo”. The third\r\nauthor was partly funded by the Austrian Science Fund (FWF) project F 65.","author":[{"first_name":"Franco","last_name":"Flandoli","full_name":"Flandoli, Franco"},{"last_name":"Priola","full_name":"Priola, Enrico","first_name":"Enrico"},{"id":"47491882-F248-11E8-B48F-1D18A9856A87","first_name":"Giovanni A","last_name":"Zanco","full_name":"Zanco, Giovanni A"}],"article_processing_charge":"No","external_id":{"arxiv":["1708.04156"],"isi":["000459954800003"]},"title":"A mean-field model with discontinuous coefficients for neurons with spatial interaction","citation":{"ista":"Flandoli F, Priola E, Zanco GA. 2019. A mean-field model with discontinuous coefficients for neurons with spatial interaction. Discrete and Continuous Dynamical Systems. 39(6), 3037–3067.","chicago":"Flandoli, Franco, Enrico Priola, and Giovanni A Zanco. “A Mean-Field Model with Discontinuous Coefficients for Neurons with Spatial Interaction.” Discrete and Continuous Dynamical Systems. American Institute of Mathematical Sciences, 2019. https://doi.org/10.3934/dcds.2019126.","ama":"Flandoli F, Priola E, Zanco GA. A mean-field model with discontinuous coefficients for neurons with spatial interaction. Discrete and Continuous Dynamical Systems. 2019;39(6):3037-3067. doi:10.3934/dcds.2019126","apa":"Flandoli, F., Priola, E., & Zanco, G. A. (2019). A mean-field model with discontinuous coefficients for neurons with spatial interaction. Discrete and Continuous Dynamical Systems. American Institute of Mathematical Sciences. https://doi.org/10.3934/dcds.2019126","short":"F. Flandoli, E. Priola, G.A. Zanco, Discrete and Continuous Dynamical Systems 39 (2019) 3037–3067.","ieee":"F. Flandoli, E. Priola, and G. A. Zanco, “A mean-field model with discontinuous coefficients for neurons with spatial interaction,” Discrete and Continuous Dynamical Systems, vol. 39, no. 6. American Institute of Mathematical Sciences, pp. 3037–3067, 2019.","mla":"Flandoli, Franco, et al. “A Mean-Field Model with Discontinuous Coefficients for Neurons with Spatial Interaction.” Discrete and Continuous Dynamical Systems, vol. 39, no. 6, American Institute of Mathematical Sciences, 2019, pp. 3037–67, doi:10.3934/dcds.2019126."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}]},{"oa":1,"quality_controlled":"1","publisher":"Springer","publication":"Calculus of Variations and Partial Differential Equations","day":"01","year":"2019","has_accepted_license":"1","isi":1,"date_created":"2018-12-11T11:44:29Z","date_published":"2019-02-01T00:00:00Z","doi":"10.1007/s00526-018-1456-1","article_number":"19","project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"_id":"260482E2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Taming Complexity in Partial Di erential Systems","grant_number":" F06504"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Erbar M, Maas J, Wirth M. 2019. On the geometry of geodesics in discrete optimal transport. Calculus of Variations and Partial Differential Equations. 58(1), 19.","chicago":"Erbar, Matthias, Jan Maas, and Melchior Wirth. “On the Geometry of Geodesics in Discrete Optimal Transport.” Calculus of Variations and Partial Differential Equations. Springer, 2019. https://doi.org/10.1007/s00526-018-1456-1.","ama":"Erbar M, Maas J, Wirth M. On the geometry of geodesics in discrete optimal transport. Calculus of Variations and Partial Differential Equations. 2019;58(1). doi:10.1007/s00526-018-1456-1","apa":"Erbar, M., Maas, J., & Wirth, M. (2019). On the geometry of geodesics in discrete optimal transport. Calculus of Variations and Partial Differential Equations. Springer. https://doi.org/10.1007/s00526-018-1456-1","ieee":"M. Erbar, J. Maas, and M. Wirth, “On the geometry of geodesics in discrete optimal transport,” Calculus of Variations and Partial Differential Equations, vol. 58, no. 1. Springer, 2019.","short":"M. Erbar, J. Maas, M. Wirth, Calculus of Variations and Partial Differential Equations 58 (2019).","mla":"Erbar, Matthias, et al. “On the Geometry of Geodesics in Discrete Optimal Transport.” Calculus of Variations and Partial Differential Equations, vol. 58, no. 1, 19, Springer, 2019, doi:10.1007/s00526-018-1456-1."},"title":"On the geometry of geodesics in discrete optimal transport","external_id":{"arxiv":["1805.06040"],"isi":["000452849400001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Matthias","last_name":"Erbar","full_name":"Erbar, Matthias"},{"last_name":"Maas","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Wirth","full_name":"Wirth, Melchior","first_name":"Melchior"}],"oa_version":"Published Version","abstract":[{"text":"We consider the space of probability measures on a discrete set X, endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset Y⊆X, it is natural to ask whether they can be connected by a constant speed geodesic with support in Y at all times. Our main result answers this question affirmatively, under a suitable geometric condition on Y introduced in this paper. The proof relies on an extension result for subsolutions to discrete Hamilton-Jacobi equations, which is of independent interest.","lang":"eng"}],"intvolume":" 58","month":"02","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"ba05ac2d69de4c58d2cd338b63512798","file_id":"5895","date_updated":"2020-07-14T12:47:55Z","file_size":645565,"creator":"dernst","date_created":"2019-01-28T15:37:11Z","file_name":"2018_Calculus_Erbar.pdf"}],"publication_status":"published","publication_identifier":{"issn":["09442669"]},"ec_funded":1,"volume":58,"issue":"1","_id":"73","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","ddc":["510"],"date_updated":"2023-09-13T09:12:35Z","department":[{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:47:55Z"},{"citation":{"mla":"Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 3, Institute of Mathematical Statistics, 2019, pp. 1203–25, doi:10.1214/18-AIHP916.","short":"P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.","ieee":"P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle in TASEP with non-random initial condition,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 3. Institute of Mathematical Statistics, pp. 1203–1225, 2019.","ama":"Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2019;55(3):1203-1225. doi:10.1214/18-AIHP916","apa":"Ferrari, P., Ghosal, P., & Nejjar, P. (2019). Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AIHP916","chicago":"Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AIHP916.","ista":"Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 55(3), 1203–1225."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"arxiv":["1710.02323"],"isi":["000487763200001"]},"author":[{"full_name":"Ferrari, Patrick","last_name":"Ferrari","first_name":"Patrick"},{"first_name":"Promit","last_name":"Ghosal","full_name":"Ghosal, Promit"},{"full_name":"Nejjar, Peter","last_name":"Nejjar","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter"}],"title":"Limit law of a second class particle in TASEP with non-random initial condition","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"year":"2019","isi":1,"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","day":"25","page":"1203-1225","date_created":"2018-12-11T11:44:29Z","doi":"10.1214/18-AIHP916","date_published":"2019-09-25T00:00:00Z","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","date_updated":"2023-10-17T08:53:45Z","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"_id":"72","type":"journal_article","article_type":"original","status":"public","publication_status":"published","publication_identifier":{"issn":["0246-0203"]},"language":[{"iso":"eng"}],"ec_funded":1,"issue":"3","volume":55,"abstract":[{"text":"We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle initially at the origin. For ρ<λ, there is a shock and the second class particle moves with speed 1−λ−ρ. For large time t, we show that the position of the second class particle fluctuates on a t1/3 scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time t.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1710.02323"}],"scopus_import":"1","intvolume":" 55","month":"09"},{"oa_version":"Published Version","abstract":[{"text":"Two generalizations of Itô formula to infinite-dimensional spaces are given.\r\nThe first one, in Hilbert spaces, extends the classical one by taking advantage of\r\ncancellations when they occur in examples and it is applied to the case of a group\r\ngenerator. The second one, based on the previous one and a limit procedure, is an Itô\r\nformula in a special class of Banach spaces having a product structure with the noise\r\nin a Hilbert component; again the key point is the extension due to a cancellation. This\r\nextension to Banach spaces and in particular the specific cancellation are motivated\r\nby path-dependent Itô calculus.","lang":"eng"}],"month":"06","intvolume":" 31","scopus_import":1,"file":[{"checksum":"47686d58ec21c164540f1a980ff2163f","file_id":"5266","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"IST-2016-712-v1+1_s10959-016-0724-2.pdf","date_created":"2018-12-12T10:17:13Z","file_size":671125,"date_updated":"2020-07-14T12:44:39Z","creator":"system"}],"language":[{"iso":"eng"}],"publication_status":"published","issue":"2","volume":31,"_id":"1215","status":"public","pubrep_id":"712","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["519"],"date_updated":"2021-01-12T06:49:09Z","file_date_updated":"2020-07-14T12:44:39Z","department":[{"_id":"JaMa"}],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The second named author benefited partially from the support of the “FMJH Program Gaspard Monge in Optimization and Operations Research” (Project 2014-1607H). He is also grateful for the invitation to the Department of Mathematics of the University of Pisa. The third named author is grateful for the invitation to ENSTA.","publisher":"Springer","quality_controlled":"1","oa":1,"day":"01","publication":"Journal of Theoretical Probability","has_accepted_license":"1","year":"2018","doi":"10.1007/s10959-016-0724-2","date_published":"2018-06-01T00:00:00Z","date_created":"2018-12-11T11:50:45Z","page":"789-826","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Flandoli, Franco, Francesco Russo, and Giovanni A Zanco. “Infinite-Dimensional Calculus under Weak Spatial Regularity of the Processes.” Journal of Theoretical Probability. Springer, 2018. https://doi.org/10.1007/s10959-016-0724-2.","ista":"Flandoli F, Russo F, Zanco GA. 2018. Infinite-dimensional calculus under weak spatial regularity of the processes. Journal of Theoretical Probability. 31(2), 789–826.","mla":"Flandoli, Franco, et al. “Infinite-Dimensional Calculus under Weak Spatial Regularity of the Processes.” Journal of Theoretical Probability, vol. 31, no. 2, Springer, 2018, pp. 789–826, doi:10.1007/s10959-016-0724-2.","ieee":"F. Flandoli, F. Russo, and G. A. Zanco, “Infinite-dimensional calculus under weak spatial regularity of the processes,” Journal of Theoretical Probability, vol. 31, no. 2. Springer, pp. 789–826, 2018.","short":"F. Flandoli, F. Russo, G.A. Zanco, Journal of Theoretical Probability 31 (2018) 789–826.","ama":"Flandoli F, Russo F, Zanco GA. Infinite-dimensional calculus under weak spatial regularity of the processes. Journal of Theoretical Probability. 2018;31(2):789-826. doi:10.1007/s10959-016-0724-2","apa":"Flandoli, F., Russo, F., & Zanco, G. A. (2018). Infinite-dimensional calculus under weak spatial regularity of the processes. Journal of Theoretical Probability. Springer. https://doi.org/10.1007/s10959-016-0724-2"},"title":"Infinite-dimensional calculus under weak spatial regularity of the processes","author":[{"last_name":"Flandoli","full_name":"Flandoli, Franco","first_name":"Franco"},{"first_name":"Francesco","full_name":"Russo, Francesco","last_name":"Russo"},{"id":"47491882-F248-11E8-B48F-1D18A9856A87","first_name":"Giovanni A","full_name":"Zanco, Giovanni A","last_name":"Zanco"}],"publist_id":"6119","article_processing_charge":"Yes (via OA deal)"},{"article_number":"e7","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge University Press, 2018.","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).","apa":"Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2018.7","ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7","mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6, e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7.","ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma. Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7."},"title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve","article_processing_charge":"No","external_id":{"arxiv":["1712.10205"],"isi":["000433915500001"]},"author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Avvakumov","full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey"}],"oa":1,"publisher":"Cambridge University Press","quality_controlled":"1","publication":"Forum of Mathematics, Sigma","day":"31","year":"2018","has_accepted_license":"1","isi":1,"date_created":"2019-04-30T06:09:57Z","date_published":"2018-05-31T00:00:00Z","doi":"10.1017/fms.2018.7","_id":"6355","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","ddc":["510"],"date_updated":"2023-09-19T14:50:12Z","file_date_updated":"2020-07-14T12:47:28Z","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"oa_version":"Published Version","abstract":[{"text":"We prove that any cyclic quadrilateral can be inscribed in any closed convex C1-curve. The smoothness condition is not required if the quadrilateral is a rectangle.","lang":"eng"}],"intvolume":" 6","month":"05","language":[{"iso":"eng"}],"file":[{"date_created":"2019-04-30T06:14:58Z","file_name":"2018_ForumMahtematics_Akopyan.pdf","date_updated":"2020-07-14T12:47:28Z","file_size":249246,"creator":"dernst","file_id":"6356","checksum":"5a71b24ba712a3eb2e46165a38fbc30a","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"publication_status":"published","publication_identifier":{"issn":["2050-5094"]},"ec_funded":1,"volume":6,"related_material":{"record":[{"relation":"dissertation_contains","id":"8156","status":"public"}]}},{"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"external_id":{"isi":["000460475800022"],"arxiv":["1705.08836"]},"article_processing_charge":"No","author":[{"first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","last_name":"Nejjar","full_name":"Nejjar, Peter"}],"title":"Transition to shocks in TASEP and decoupling of last passage times","citation":{"ista":"Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 15(2), 1311–1334.","chicago":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada, 2018. https://doi.org/10.30757/ALEA.v15-49.","ieee":"P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.","short":"P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334.","ama":"Nejjar P. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 2018;15(2):1311-1334. doi:10.30757/ALEA.v15-49","apa":"Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v15-49","mla":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34, doi:10.30757/ALEA.v15-49."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"quality_controlled":"1","publisher":"Instituto Nacional de Matematica Pura e Aplicada","page":"1311-1334","date_created":"2018-12-11T11:44:28Z","date_published":"2018-10-01T00:00:00Z","doi":"10.30757/ALEA.v15-49","year":"2018","has_accepted_license":"1","isi":1,"publication":"Latin American Journal of Probability and Mathematical Statistics","day":"01","article_type":"original","type":"journal_article","status":"public","_id":"70","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:47:46Z","date_updated":"2023-10-10T13:11:29Z","ddc":["510"],"scopus_import":"1","intvolume":" 15","month":"10","abstract":[{"text":"We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by a≥0, which creates a shock in the particle density of order aT−1/3, T the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit lima→∞limT→∞ one recovers the product limit law and the degeneration of the correlation length observed at shocks of order 1. This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several airy processes.","lang":"eng"}],"oa_version":"Published Version","ec_funded":1,"issue":"2","volume":15,"publication_status":"published","publication_identifier":{"issn":["1980-0436"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"2ded46aa284a836a8cbb34133a64f1cb","file_id":"5981","date_updated":"2020-07-14T12:47:46Z","file_size":394851,"creator":"kschuh","date_created":"2019-02-14T09:44:10Z","file_name":"2018_ALEA_Nejjar.pdf"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-12-18T10:51:02Z","citation":{"chicago":"Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions into Arbitrary Number of Pieces.” arXiv, 2018. https://doi.org/10.48550/arXiv.1804.03057.","ista":"Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 1804.03057.","mla":"Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057.","apa":"Akopyan, A., Avvakumov, S., & Karasev, R. (2018). Convex fair partitions into arbitrary number of pieces. arXiv. https://doi.org/10.48550/arXiv.1804.03057","ama":"Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 2018. doi:10.48550/arXiv.1804.03057","ieee":"A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018.","short":"A. Akopyan, S. Avvakumov, R. Karasev, (2018)."},"department":[{"_id":"HeEd"},{"_id":"JaMa"}],"title":"Convex fair partitions into arbitrary number of pieces","author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"full_name":"Avvakumov, Sergey","last_name":"Avvakumov","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"article_processing_charge":"No","external_id":{"arxiv":["1804.03057"]},"article_number":"1804.03057","_id":"75","status":"public","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}],"type":"preprint","day":"13","language":[{"iso":"eng"}],"year":"2018","publication_status":"published","related_material":{"record":[{"relation":"dissertation_contains","id":"8156","status":"public"}]},"doi":"10.48550/arXiv.1804.03057","date_published":"2018-09-13T00:00:00Z","ec_funded":1,"date_created":"2018-12-11T11:44:30Z","oa_version":"Preprint","abstract":[{"lang":"eng","text":"We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and perimeters for any integer m≥2; this result was previously known for prime powers m=pk. We also give a higher-dimensional generalization."}],"month":"09","publisher":"arXiv","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1804.03057","open_access":"1"}]},{"quality_controlled":"1","publisher":"Springer Nature","oa":1,"doi":"10.1007/s00023-018-0723-1","date_published":"2018-11-13T00:00:00Z","date_created":"2018-12-11T11:47:09Z","page":"3663-3742","day":"13","publication":"Annales Henri Poincare","has_accepted_license":"1","year":"2018","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"title":"The free boundary Schur process and applications I","publist_id":"7258","author":[{"last_name":"Betea","full_name":"Betea, Dan","first_name":"Dan"},{"full_name":"Bouttier, Jeremie","last_name":"Bouttier","first_name":"Jeremie"},{"full_name":"Nejjar, Peter","last_name":"Nejjar","first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Vuletic","full_name":"Vuletic, Mirjana","first_name":"Mirjana"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["1704.05809"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Betea D, Bouttier J, Nejjar P, Vuletic M. The free boundary Schur process and applications I. Annales Henri Poincare. 2018;19(12):3663-3742. doi:10.1007/s00023-018-0723-1","apa":"Betea, D., Bouttier, J., Nejjar, P., & Vuletic, M. (2018). The free boundary Schur process and applications I. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-018-0723-1","short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018) 3663–3742.","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletic, “The free boundary Schur process and applications I,” Annales Henri Poincare, vol. 19, no. 12. Springer Nature, pp. 3663–3742, 2018.","mla":"Betea, Dan, et al. “The Free Boundary Schur Process and Applications I.” Annales Henri Poincare, vol. 19, no. 12, Springer Nature, 2018, pp. 3663–742, doi:10.1007/s00023-018-0723-1.","ista":"Betea D, Bouttier J, Nejjar P, Vuletic M. 2018. The free boundary Schur process and applications I. Annales Henri Poincare. 19(12), 3663–3742.","chicago":"Betea, Dan, Jeremie Bouttier, Peter Nejjar, and Mirjana Vuletic. “The Free Boundary Schur Process and Applications I.” Annales Henri Poincare. Springer Nature, 2018. https://doi.org/10.1007/s00023-018-0723-1."},"month":"11","intvolume":" 19","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We investigate the free boundary Schur process, a variant of the Schur process introduced by Okounkov and Reshetikhin, where we allow the first and the last partitions to be arbitrary (instead of empty in the original setting). The pfaffian Schur process, previously studied by several authors, is recovered when just one of the boundary partitions is left free. We compute the correlation functions of the process in all generality via the free fermion formalism, which we extend with the thorough treatment of “free boundary states.” For the case of one free boundary, our approach yields a new proof that the process is pfaffian. For the case of two free boundaries, we find that the process is not pfaffian, but a closely related process is. We also study three different applications of the Schur process with one free boundary: fluctuations of symmetrized last passage percolation models, limit shapes and processes for symmetric plane partitions and for plane overpartitions."}],"issue":"12","volume":19,"ec_funded":1,"file":[{"file_name":"2018_Annales_Betea.pdf","date_created":"2019-01-21T15:18:55Z","creator":"dernst","file_size":3084674,"date_updated":"2020-07-14T12:47:03Z","checksum":"0c38abe73569b7166b7487ad5d23cc68","file_id":"5866","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1424-0637"]},"publication_status":"published","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"556","file_date_updated":"2020-07-14T12:47:03Z","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"ddc":["500"],"date_updated":"2024-02-20T10:48:17Z"},{"status":"public","type":"journal_article","_id":"560","department":[{"_id":"JaMa"}],"date_updated":"2021-01-12T08:03:04Z","intvolume":" 473","month":"11","main_file_link":[{"url":"https://arxiv.org/abs/1702.03229","open_access":"1"}],"scopus_import":1,"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"In a recent article (Jentzen et al. 2016 Commun. Math. Sci. 14, 1477–1500 (doi:10.4310/CMS.2016.v14. n6.a1)), it has been established that, for every arbitrarily slow convergence speed and every natural number d ? {4, 5, . . .}, there exist d-dimensional stochastic differential equations with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of convergence. In this paper, we strengthen the above result by proving that this slow convergence phenomenon also arises in two (d = 2) and three (d = 3) space dimensions."}],"ec_funded":1,"volume":473,"issue":"2207","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["13645021"]},"project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"article_number":"0104","title":"On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions","author":[{"full_name":"Gerencser, Mate","last_name":"Gerencser","first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Arnulf","last_name":"Jentzen","full_name":"Jentzen, Arnulf"},{"last_name":"Salimova","full_name":"Salimova, Diyora","first_name":"Diyora"}],"publist_id":"7256","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Gerencser, Mate, Arnulf Jentzen, and Diyora Salimova. “On Stochastic Differential Equations with Arbitrarily Slow Convergence Rates for Strong Approximation in Two Space Dimensions.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. Royal Society of London, 2017. https://doi.org/10.1098/rspa.2017.0104.","ista":"Gerencser M, Jentzen A, Salimova D. 2017. On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 473(2207), 0104.","mla":"Gerencser, Mate, et al. “On Stochastic Differential Equations with Arbitrarily Slow Convergence Rates for Strong Approximation in Two Space Dimensions.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 473, no. 2207, 0104, Royal Society of London, 2017, doi:10.1098/rspa.2017.0104.","short":"M. Gerencser, A. Jentzen, D. Salimova, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473 (2017).","ieee":"M. Gerencser, A. Jentzen, and D. Salimova, “On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 473, no. 2207. Royal Society of London, 2017.","ama":"Gerencser M, Jentzen A, Salimova D. On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2017;473(2207). doi:10.1098/rspa.2017.0104","apa":"Gerencser, M., Jentzen, A., & Salimova, D. (2017). On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. Royal Society of London. https://doi.org/10.1098/rspa.2017.0104"},"oa":1,"publisher":"Royal Society of London","quality_controlled":"1","date_created":"2018-12-11T11:47:11Z","doi":"10.1098/rspa.2017.0104","date_published":"2017-11-01T00:00:00Z","publication":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","day":"01","year":"2017"},{"doi":"10.1090/mcom/3201","date_published":"2017-01-01T00:00:00Z","date_created":"2018-12-11T11:47:40Z","page":"2373 - 2397","day":"01","publication":"Mathematics of Computation","year":"2017","publisher":"American Mathematical Society","quality_controlled":"1","oa":1,"title":"Localization errors in solving stochastic partial differential equations in the whole space","publist_id":"7144","author":[{"first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87","full_name":"Gerencser, Mate","last_name":"Gerencser"},{"first_name":"István","last_name":"Gyöngy","full_name":"Gyöngy, István"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Gerencser, Mate, and István Gyöngy. “Localization Errors in Solving Stochastic Partial Differential Equations in the Whole Space.” Mathematics of Computation, vol. 86, no. 307, American Mathematical Society, 2017, pp. 2373–97, doi:10.1090/mcom/3201.","ieee":"M. Gerencser and I. Gyöngy, “Localization errors in solving stochastic partial differential equations in the whole space,” Mathematics of Computation, vol. 86, no. 307. American Mathematical Society, pp. 2373–2397, 2017.","short":"M. Gerencser, I. Gyöngy, Mathematics of Computation 86 (2017) 2373–2397.","apa":"Gerencser, M., & Gyöngy, I. (2017). Localization errors in solving stochastic partial differential equations in the whole space. Mathematics of Computation. American Mathematical Society. https://doi.org/10.1090/mcom/3201","ama":"Gerencser M, Gyöngy I. Localization errors in solving stochastic partial differential equations in the whole space. Mathematics of Computation. 2017;86(307):2373-2397. doi:10.1090/mcom/3201","chicago":"Gerencser, Mate, and István Gyöngy. “Localization Errors in Solving Stochastic Partial Differential Equations in the Whole Space.” Mathematics of Computation. American Mathematical Society, 2017. https://doi.org/10.1090/mcom/3201.","ista":"Gerencser M, Gyöngy I. 2017. Localization errors in solving stochastic partial differential equations in the whole space. Mathematics of Computation. 86(307), 2373–2397."},"volume":86,"issue":"307","language":[{"iso":"eng"}],"publication_identifier":{"issn":["00255718"]},"publication_status":"published","month":"01","intvolume":" 86","scopus_import":1,"main_file_link":[{"url":"https://arxiv.org/abs/1508.05535","open_access":"1"}],"oa_version":"Submitted Version","abstract":[{"text":"Cauchy problems with SPDEs on the whole space are localized to Cauchy problems on a ball of radius R. This localization reduces various kinds of spatial approximation schemes to finite dimensional problems. The error is shown to be exponentially small. As an application, a numerical scheme is presented which combines the localization and the space and time discretization, and thus is fully implementable.","lang":"eng"}],"department":[{"_id":"JaMa"}],"date_updated":"2021-01-12T08:07:26Z","status":"public","type":"journal_article","_id":"642"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Maas, Jan. “Entropic Ricci Curvature for Discrete Spaces.” In Modern Approaches to Discrete Curvature, edited by Laurent Najman and Pascal Romon, 2184:159–74. Lecture Notes in Mathematics. Springer, 2017. https://doi.org/10.1007/978-3-319-58002-9_5.","ista":"Maas J. 2017.Entropic Ricci curvature for discrete spaces. In: Modern Approaches to Discrete Curvature. vol. 2184, 159–174.","mla":"Maas, Jan. “Entropic Ricci Curvature for Discrete Spaces.” Modern Approaches to Discrete Curvature, edited by Laurent Najman and Pascal Romon, vol. 2184, Springer, 2017, pp. 159–74, doi:10.1007/978-3-319-58002-9_5.","ieee":"J. Maas, “Entropic Ricci curvature for discrete spaces,” in Modern Approaches to Discrete Curvature, vol. 2184, L. Najman and P. Romon, Eds. Springer, 2017, pp. 159–174.","short":"J. Maas, in:, L. Najman, P. Romon (Eds.), Modern Approaches to Discrete Curvature, Springer, 2017, pp. 159–174.","apa":"Maas, J. (2017). Entropic Ricci curvature for discrete spaces. In L. Najman & P. Romon (Eds.), Modern Approaches to Discrete Curvature (Vol. 2184, pp. 159–174). Springer. https://doi.org/10.1007/978-3-319-58002-9_5","ama":"Maas J. Entropic Ricci curvature for discrete spaces. In: Najman L, Romon P, eds. Modern Approaches to Discrete Curvature. Vol 2184. Lecture Notes in Mathematics. Springer; 2017:159-174. doi:10.1007/978-3-319-58002-9_5"},"editor":[{"full_name":"Najman, Laurent","last_name":"Najman","first_name":"Laurent"},{"full_name":"Romon, Pascal","last_name":"Romon","first_name":"Pascal"}],"title":"Entropic Ricci curvature for discrete spaces","article_processing_charge":"No","author":[{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas"}],"publist_id":"7123","publication":"Modern Approaches to Discrete Curvature","day":"05","year":"2017","date_created":"2018-12-11T11:47:42Z","date_published":"2017-10-05T00:00:00Z","doi":"10.1007/978-3-319-58002-9_5","page":"159 - 174","quality_controlled":"1","publisher":"Springer","date_updated":"2022-05-24T07:01:33Z","department":[{"_id":"JaMa"}],"_id":"649","series_title":"Lecture Notes in Mathematics","status":"public","type":"book_chapter","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"isbn":["978-3-319-58001-2"],"eissn":["978-3-319-58002-9"]},"volume":2184,"oa_version":"None","abstract":[{"lang":"eng","text":"We give a short overview on a recently developed notion of Ricci curvature for discrete spaces. This notion relies on geodesic convexity properties of the relative entropy along geodesics in the space of probability densities, for a metric which is similar to (but different from) the 2-Wasserstein metric. The theory can be considered as a discrete counterpart to the theory of Ricci curvature for geodesic measure spaces developed by Lott–Sturm–Villani."}],"intvolume":" 2184","month":"10","scopus_import":"1"},{"day":"18","year":"2017","isi":1,"date_created":"2018-12-11T11:49:34Z","date_published":"2017-05-18T00:00:00Z","doi":"10.1007/978-3-319-58771-4_45","page":"563 - 577","publisher":"Springer","quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"apa":"Maas, J., Rumpf, M., & Simon, S. (2017). Transport based image morphing with intensity modulation. In F. Lauze, Y. Dong, & A. Bjorholm Dahl (Eds.) (Vol. 10302, pp. 563–577). Presented at the SSVM: Scale Space and Variational Methods in Computer Vision, Kolding, Denmark: Springer. https://doi.org/10.1007/978-3-319-58771-4_45","ama":"Maas J, Rumpf M, Simon S. Transport based image morphing with intensity modulation. In: Lauze F, Dong Y, Bjorholm Dahl A, eds. Vol 10302. Springer; 2017:563-577. doi:10.1007/978-3-319-58771-4_45","ieee":"J. Maas, M. Rumpf, and S. Simon, “Transport based image morphing with intensity modulation,” presented at the SSVM: Scale Space and Variational Methods in Computer Vision, Kolding, Denmark, 2017, vol. 10302, pp. 563–577.","short":"J. Maas, M. Rumpf, S. Simon, in:, F. Lauze, Y. Dong, A. Bjorholm Dahl (Eds.), Springer, 2017, pp. 563–577.","mla":"Maas, Jan, et al. Transport Based Image Morphing with Intensity Modulation. Edited by François Lauze et al., vol. 10302, Springer, 2017, pp. 563–77, doi:10.1007/978-3-319-58771-4_45.","ista":"Maas J, Rumpf M, Simon S. 2017. Transport based image morphing with intensity modulation. SSVM: Scale Space and Variational Methods in Computer Vision, LNCS, vol. 10302, 563–577.","chicago":"Maas, Jan, Martin Rumpf, and Stefan Simon. “Transport Based Image Morphing with Intensity Modulation.” edited by François Lauze, Yiqiu Dong, and Anders Bjorholm Dahl, 10302:563–77. Springer, 2017. https://doi.org/10.1007/978-3-319-58771-4_45."},"title":"Transport based image morphing with intensity modulation","editor":[{"last_name":"Lauze","full_name":"Lauze, François","first_name":"François"},{"first_name":"Yiqiu","last_name":"Dong","full_name":"Dong, Yiqiu"},{"full_name":"Bjorholm Dahl, Anders","last_name":"Bjorholm Dahl","first_name":"Anders"}],"external_id":{"isi":["000432210900045"]},"article_processing_charge":"No","publist_id":"6410","author":[{"first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas"},{"full_name":"Rumpf, Martin","last_name":"Rumpf","first_name":"Martin"},{"first_name":"Stefan","last_name":"Simon","full_name":"Simon, Stefan"}],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["03029743"]},"volume":10302,"oa_version":"None","abstract":[{"text":"We present a generalized optimal transport model in which the mass-preserving constraint for the L2-Wasserstein distance is relaxed by introducing a source term in the continuity equation. The source term is also incorporated in the path energy by means of its squared L2-norm in time of a functional with linear growth in space. This extension of the original transport model enables local density modulations, which is a desirable feature in applications such as image warping and blending. A key advantage of the use of a functional with linear growth in space is that it allows for singular sources and sinks, which can be supported on points or lines. On a technical level, the L2-norm in time ensures a disintegration of the source in time, which we use to obtain the well-posedness of the model and the existence of geodesic paths. The numerical discretization is based on the proximal splitting approach [18] and selected numerical test cases show the potential of the proposed approach. Furthermore, the approach is applied to the warping and blending of textures.","lang":"eng"}],"intvolume":" 10302","month":"05","scopus_import":"1","alternative_title":["LNCS"],"date_updated":"2023-09-22T09:55:50Z","department":[{"_id":"JaMa"}],"_id":"989","status":"public","conference":{"end_date":"2017-06-08","location":"Kolding, Denmark","start_date":"2017-06-04","name":"SSVM: Scale Space and Variational Methods in Computer Vision"},"type":"conference"},{"oa":1,"publisher":"Academic Press","quality_controlled":"1","year":"2017","isi":1,"publication":"Journal of Functional Analysis","day":"01","page":"1810 - 1869","date_created":"2018-12-11T11:49:24Z","date_published":"2017-09-01T00:00:00Z","doi":"10.1016/j.jfa.2017.05.003","citation":{"ista":"Carlen E, Maas J. 2017. Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance. Journal of Functional Analysis. 273(5), 1810–1869.","chicago":"Carlen, Eric, and Jan Maas. “Gradient Flow and Entropy Inequalities for Quantum Markov Semigroups with Detailed Balance.” Journal of Functional Analysis. Academic Press, 2017. https://doi.org/10.1016/j.jfa.2017.05.003.","ieee":"E. Carlen and J. Maas, “Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance,” Journal of Functional Analysis, vol. 273, no. 5. Academic Press, pp. 1810–1869, 2017.","short":"E. Carlen, J. Maas, Journal of Functional Analysis 273 (2017) 1810–1869.","ama":"Carlen E, Maas J. Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance. Journal of Functional Analysis. 2017;273(5):1810-1869. doi:10.1016/j.jfa.2017.05.003","apa":"Carlen, E., & Maas, J. (2017). Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance. Journal of Functional Analysis. Academic Press. https://doi.org/10.1016/j.jfa.2017.05.003","mla":"Carlen, Eric, and Jan Maas. “Gradient Flow and Entropy Inequalities for Quantum Markov Semigroups with Detailed Balance.” Journal of Functional Analysis, vol. 273, no. 5, Academic Press, 2017, pp. 1810–69, doi:10.1016/j.jfa.2017.05.003."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","external_id":{"isi":["000406082300005"]},"author":[{"last_name":"Carlen","full_name":"Carlen, Eric","first_name":"Eric"},{"last_name":"Maas","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"}],"publist_id":"6452","title":"Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance","abstract":[{"text":"We study a class of ergodic quantum Markov semigroups on finite-dimensional unital C⁎-algebras. These semigroups have a unique stationary state σ, and we are concerned with those that satisfy a quantum detailed balance condition with respect to σ. We show that the evolution on the set of states that is given by such a quantum Markov semigroup is gradient flow for the relative entropy with respect to σ in a particular Riemannian metric on the set of states. This metric is a non-commutative analog of the 2-Wasserstein metric, and in several interesting cases we are able to show, in analogy with work of Otto on gradient flows with respect to the classical 2-Wasserstein metric, that the relative entropy is strictly and uniformly convex with respect to the Riemannian metric introduced here. As a consequence, we obtain a number of new inequalities for the decay of relative entropy for ergodic quantum Markov semigroups with detailed balance.","lang":"eng"}],"oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1609.01254"}],"scopus_import":"1","intvolume":" 273","month":"09","publication_status":"published","publication_identifier":{"issn":["00221236"]},"language":[{"iso":"eng"}],"volume":273,"issue":"5","_id":"956","type":"journal_article","status":"public","date_updated":"2023-09-22T10:00:18Z","department":[{"_id":"JaMa"}]},{"title":"Fluctuations of the competition interface in presence of shocks","publist_id":"7376","author":[{"first_name":"Patrik","last_name":"Ferrari","full_name":"Ferrari, Patrik"},{"first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","full_name":"Nejjar, Peter","last_name":"Nejjar"}],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Ferrari, Patrik, and Peter Nejjar. “Fluctuations of the Competition Interface in Presence of Shocks.” Revista Latino-Americana de Probabilidade e Estatística, vol. 9, Instituto Nacional de Matematica Pura e Aplicada, 2017, pp. 299–325, doi:10.30757/ALEA.v14-17.","ieee":"P. Ferrari and P. Nejjar, “Fluctuations of the competition interface in presence of shocks,” Revista Latino-Americana de Probabilidade e Estatística, vol. 9. Instituto Nacional de Matematica Pura e Aplicada, pp. 299–325, 2017.","short":"P. Ferrari, P. Nejjar, Revista Latino-Americana de Probabilidade e Estatística 9 (2017) 299–325.","apa":"Ferrari, P., & Nejjar, P. (2017). Fluctuations of the competition interface in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística. Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v14-17","ama":"Ferrari P, Nejjar P. Fluctuations of the competition interface in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística. 2017;9:299-325. doi:10.30757/ALEA.v14-17","chicago":"Ferrari, Patrik, and Peter Nejjar. “Fluctuations of the Competition Interface in Presence of Shocks.” Revista Latino-Americana de Probabilidade e Estatística. Instituto Nacional de Matematica Pura e Aplicada, 2017. https://doi.org/10.30757/ALEA.v14-17.","ista":"Ferrari P, Nejjar P. 2017. Fluctuations of the competition interface in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística. 9, 299–325."},"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"date_published":"2017-03-23T00:00:00Z","doi":"10.30757/ALEA.v14-17","date_created":"2018-12-11T11:46:31Z","page":"299 - 325","day":"23","publication":"Revista Latino-Americana de Probabilidade e Estatística","year":"2017","publisher":"Instituto Nacional de Matematica Pura e Aplicada","quality_controlled":"1","oa":1,"department":[{"_id":"LaEr"},{"_id":"JaMa"}],"date_updated":"2023-10-10T13:10:32Z","status":"public","article_type":"original","type":"journal_article","_id":"447","volume":9,"ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","month":"03","intvolume":" 9","scopus_import":"1","main_file_link":[{"open_access":"1","url":"http://alea.impa.br/articles/v14/14-17.pdf"}],"oa_version":"Submitted Version","abstract":[{"text":"We consider last passage percolation (LPP) models with exponentially distributed random variables, which are linked to the totally asymmetric simple exclusion process (TASEP). The competition interface for LPP was introduced and studied in Ferrari and Pimentel (2005a) for cases where the corresponding exclusion process had a rarefaction fan. Here we consider situations with a shock and determine the law of the fluctuations of the competition interface around its deter- ministic law of large number position. We also study the multipoint distribution of the LPP around the shock, extending our one-point result of Ferrari and Nejjar (2015).","lang":"eng"}]},{"oa":1,"publisher":"IOP Publishing Ltd.","quality_controlled":"1","acknowledgement":"This research was supported by the DFG Collaborative Research Centers TRR 109, ‘ Discretization in Geometry and Dynamics ’ and 1060 ‘ The Mathematics of Emergent Effects ’ .","page":"1992 - 2023","date_created":"2018-12-11T11:51:00Z","date_published":"2016-06-10T00:00:00Z","doi":"10.1088/0951-7715/29/7/1992","year":"2016","publication":"Nonlinearity","day":"10","publist_id":"6062","author":[{"last_name":"Maas","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"},{"first_name":"Daniel","full_name":"Matthes, Daniel","last_name":"Matthes"}],"title":"Long-time behavior of a finite volume discretization for a fourth order diffusion equation","citation":{"mla":"Maas, Jan, and Daniel Matthes. “Long-Time Behavior of a Finite Volume Discretization for a Fourth Order Diffusion Equation.” Nonlinearity, vol. 29, no. 7, IOP Publishing Ltd., 2016, pp. 1992–2023, doi:10.1088/0951-7715/29/7/1992.","ama":"Maas J, Matthes D. Long-time behavior of a finite volume discretization for a fourth order diffusion equation. Nonlinearity. 2016;29(7):1992-2023. doi:10.1088/0951-7715/29/7/1992","apa":"Maas, J., & Matthes, D. (2016). Long-time behavior of a finite volume discretization for a fourth order diffusion equation. Nonlinearity. IOP Publishing Ltd. https://doi.org/10.1088/0951-7715/29/7/1992","short":"J. Maas, D. Matthes, Nonlinearity 29 (2016) 1992–2023.","ieee":"J. Maas and D. Matthes, “Long-time behavior of a finite volume discretization for a fourth order diffusion equation,” Nonlinearity, vol. 29, no. 7. IOP Publishing Ltd., pp. 1992–2023, 2016.","chicago":"Maas, Jan, and Daniel Matthes. “Long-Time Behavior of a Finite Volume Discretization for a Fourth Order Diffusion Equation.” Nonlinearity. IOP Publishing Ltd., 2016. https://doi.org/10.1088/0951-7715/29/7/1992.","ista":"Maas J, Matthes D. 2016. Long-time behavior of a finite volume discretization for a fourth order diffusion equation. Nonlinearity. 29(7), 1992–2023."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/1505.03178","open_access":"1"}],"scopus_import":1,"intvolume":" 29","month":"06","abstract":[{"text":"We consider a non-standard finite-volume discretization of a strongly non-linear fourth order diffusion equation on the d-dimensional cube, for arbitrary . The scheme preserves two important structural properties of the equation: the first is the interpretation as a gradient flow in a mass transportation metric, and the second is an intimate relation to a linear Fokker-Planck equation. Thanks to these structural properties, the scheme possesses two discrete Lyapunov functionals. These functionals approximate the entropy and the Fisher information, respectively, and their dissipation rates converge to the optimal ones in the discrete-to-continuous limit. Using the dissipation, we derive estimates on the long-time asymptotics of the discrete solutions. Finally, we present results from numerical experiments which indicate that our discretization is able to capture significant features of the complex original dynamics, even with a rather coarse spatial resolution.","lang":"eng"}],"oa_version":"Preprint","volume":29,"issue":"7","publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"1261","department":[{"_id":"JaMa"}],"date_updated":"2021-01-12T06:49:28Z"},{"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets. Using different methods, such bounds have recently been obtained in several examples (e.g., 1-dimensional birth and death chains, product chains, Bernoulli–Laplace models, and random transposition models). However, a general method to obtain discrete Ricci bounds had been lacking. Our method covers all of the examples above. In addition we obtain new Ricci curvature bounds for zero-range processes on the complete graph. The method is inspired by recent work of Caputo, Dai Pra and Posta on discrete functional inequalities."}],"intvolume":" 26","month":"06","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1501.00562"}],"scopus_import":1,"language":[{"iso":"eng"}],"publication_status":"published","volume":26,"issue":"3","_id":"1448","status":"public","type":"journal_article","date_updated":"2021-01-12T06:50:49Z","department":[{"_id":"JaMa"}],"acknowledgement":"Supported by the German Research Foundation through the Collaborative Research Center 1060\r\nThe Mathematics of Emergent Effects and the Hausdorff Center for Mathematics. Part of this work has been done while M. Fathi visited J. Maas at the University of Bonn in July 2014.We would like to thank the referees for their careful reading of the manuscript. ","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","publication":"The Annals of Applied Probability","day":"01","year":"2016","date_created":"2018-12-11T11:52:05Z","date_published":"2016-06-01T00:00:00Z","doi":"10.1214/15-AAP1133","page":"1774 - 1806","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Fathi, Max, and Jan Maas. “Entropic Ricci Curvature Bounds for Discrete Interacting Systems.” The Annals of Applied Probability. Institute of Mathematical Statistics, 2016. https://doi.org/10.1214/15-AAP1133.","ista":"Fathi M, Maas J. 2016. Entropic Ricci curvature bounds for discrete interacting systems. The Annals of Applied Probability. 26(3), 1774–1806.","mla":"Fathi, Max, and Jan Maas. “Entropic Ricci Curvature Bounds for Discrete Interacting Systems.” The Annals of Applied Probability, vol. 26, no. 3, Institute of Mathematical Statistics, 2016, pp. 1774–806, doi:10.1214/15-AAP1133.","ieee":"M. Fathi and J. Maas, “Entropic Ricci curvature bounds for discrete interacting systems,” The Annals of Applied Probability, vol. 26, no. 3. Institute of Mathematical Statistics, pp. 1774–1806, 2016.","short":"M. Fathi, J. Maas, The Annals of Applied Probability 26 (2016) 1774–1806.","apa":"Fathi, M., & Maas, J. (2016). Entropic Ricci curvature bounds for discrete interacting systems. The Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/15-AAP1133","ama":"Fathi M, Maas J. Entropic Ricci curvature bounds for discrete interacting systems. The Annals of Applied Probability. 2016;26(3):1774-1806. doi:10.1214/15-AAP1133"},"title":"Entropic Ricci curvature bounds for discrete interacting systems","publist_id":"5748","author":[{"last_name":"Fathi","full_name":"Fathi, Max","first_name":"Max"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Maas","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338"}]},{"publist_id":"5660","author":[{"last_name":"Erbar","full_name":"Erbar, Matthias","first_name":"Matthias"},{"first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas"},{"last_name":"Renger","full_name":"Renger, Michiel","first_name":"Michiel"}],"title":"From large deviations to Wasserstein gradient flows in multiple dimensions","citation":{"ista":"Erbar M, Maas J, Renger M. 2015. From large deviations to Wasserstein gradient flows in multiple dimensions. Electronic Communications in Probability. 20, 89.","chicago":"Erbar, Matthias, Jan Maas, and Michiel Renger. “From Large Deviations to Wasserstein Gradient Flows in Multiple Dimensions.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2015. https://doi.org/10.1214/ECP.v20-4315.","apa":"Erbar, M., Maas, J., & Renger, M. (2015). From large deviations to Wasserstein gradient flows in multiple dimensions. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/ECP.v20-4315","ama":"Erbar M, Maas J, Renger M. From large deviations to Wasserstein gradient flows in multiple dimensions. Electronic Communications in Probability. 2015;20. doi:10.1214/ECP.v20-4315","ieee":"M. Erbar, J. Maas, and M. Renger, “From large deviations to Wasserstein gradient flows in multiple dimensions,” Electronic Communications in Probability, vol. 20. Institute of Mathematical Statistics, 2015.","short":"M. Erbar, J. Maas, M. Renger, Electronic Communications in Probability 20 (2015).","mla":"Erbar, Matthias, et al. “From Large Deviations to Wasserstein Gradient Flows in Multiple Dimensions.” Electronic Communications in Probability, vol. 20, 89, Institute of Mathematical Statistics, 2015, doi:10.1214/ECP.v20-4315."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","article_number":"89","doi":"10.1214/ECP.v20-4315","date_published":"2015-11-29T00:00:00Z","date_created":"2018-12-11T11:52:29Z","has_accepted_license":"1","year":"2015","day":"29","publication":"Electronic Communications in Probability","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"file_date_updated":"2020-07-14T12:45:00Z","department":[{"_id":"JaMa"}],"date_updated":"2021-01-12T06:51:19Z","ddc":["519"],"type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","pubrep_id":"494","_id":"1517","volume":20,"publication_status":"published","file":[{"file_size":230525,"date_updated":"2020-07-14T12:45:00Z","creator":"system","file_name":"IST-2016-494-v1+1_4315-23820-1-PB.pdf","date_created":"2018-12-12T10:10:39Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"4828","checksum":"135741c17d3e1547ca696b6fbdcd559c"}],"language":[{"iso":"eng"}],"scopus_import":1,"month":"11","intvolume":" 20","abstract":[{"lang":"eng","text":"We study the large deviation rate functional for the empirical distribution of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier and Zimmer that this functional is asymptotically equivalent (in the sense of Γ-convergence) to the Jordan-Kinderlehrer-Otto functional arising in the Wasserstein gradient flow structure of the Fokker-Planck equation. In higher dimensions, part of this statement (the lower bound) has been recently proved by Duong, Laschos and Renger, but the upper bound remained open, since the proof of Duong et al relies on regularity properties of optimal transport maps that are restricted to one dimension. In this note we present a new proof of the upper bound, thereby generalising the result of Adams et al to arbitrary dimensions.\r\n"}],"oa_version":"Published Version"},{"_id":"1639","type":"journal_article","status":"public","date_updated":"2021-01-12T06:52:10Z","department":[{"_id":"JaMa"}],"abstract":[{"lang":"eng","text":"In this paper the optimal transport and the metamorphosis perspectives are combined. For a pair of given input images geodesic paths in the space of images are defined as minimizers of a resulting path energy. To this end, the underlying Riemannian metric measures the rate of transport cost and the rate of viscous dissipation. Furthermore, the model is capable to deal with strongly varying image contrast and explicitly allows for sources and sinks in the transport equations which are incorporated in the metric related to the metamorphosis approach by Trouvé and Younes. In the non-viscous case with source term existence of geodesic paths is proven in the space of measures. The proposed model is explored on the range from merely optimal transport to strongly dissipative dynamics. For this model a robust and effective variational time discretization of geodesic paths is proposed. This requires to minimize a discrete path energy consisting of a sum of consecutive image matching functionals. These functionals are defined on corresponding pairs of intensity functions and on associated pairwise matching deformations. Existence of time discrete geodesics is demonstrated. Furthermore, a finite element implementation is proposed and applied to instructive test cases and to real images. In the non-viscous case this is compared to the algorithm proposed by Benamou and Brenier including a discretization of the source term. Finally, the model is generalized to define discrete weighted barycentres with applications to textures and objects."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1504.01988"}],"scopus_import":1,"intvolume":" 49","month":"11","publication_status":"published","language":[{"iso":"eng"}],"issue":"6","volume":49,"citation":{"mla":"Maas, Jan, et al. “A Generalized Model for Optimal Transport of Images Including Dissipation and Density Modulation.” ESAIM: Mathematical Modelling and Numerical Analysis, vol. 49, no. 6, EDP Sciences, 2015, pp. 1745–69, doi:10.1051/m2an/2015043.","apa":"Maas, J., Rumpf, M., Schönlieb, C., & Simon, S. (2015). A generalized model for optimal transport of images including dissipation and density modulation. ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences. https://doi.org/10.1051/m2an/2015043","ama":"Maas J, Rumpf M, Schönlieb C, Simon S. A generalized model for optimal transport of images including dissipation and density modulation. ESAIM: Mathematical Modelling and Numerical Analysis. 2015;49(6):1745-1769. doi:10.1051/m2an/2015043","ieee":"J. Maas, M. Rumpf, C. Schönlieb, and S. Simon, “A generalized model for optimal transport of images including dissipation and density modulation,” ESAIM: Mathematical Modelling and Numerical Analysis, vol. 49, no. 6. EDP Sciences, pp. 1745–1769, 2015.","short":"J. Maas, M. Rumpf, C. Schönlieb, S. Simon, ESAIM: Mathematical Modelling and Numerical Analysis 49 (2015) 1745–1769.","chicago":"Maas, Jan, Martin Rumpf, Carola Schönlieb, and Stefan Simon. “A Generalized Model for Optimal Transport of Images Including Dissipation and Density Modulation.” ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences, 2015. https://doi.org/10.1051/m2an/2015043.","ista":"Maas J, Rumpf M, Schönlieb C, Simon S. 2015. A generalized model for optimal transport of images including dissipation and density modulation. ESAIM: Mathematical Modelling and Numerical Analysis. 49(6), 1745–1769."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["1504.01988"]},"publist_id":"5514","author":[{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Maas","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338"},{"first_name":"Martin","last_name":"Rumpf","full_name":"Rumpf, Martin"},{"last_name":"Schönlieb","full_name":"Schönlieb, Carola","first_name":"Carola"},{"first_name":"Stefan","full_name":"Simon, Stefan","last_name":"Simon"}],"title":"A generalized model for optimal transport of images including dissipation and density modulation","acknowledgement":"The authors acknowledge support of the Collaborative Research Centre 1060 funded by the German Science foundation. This work is further supported by the King Abdullah University for Science and Technology (KAUST) Award No. KUK-I1-007-43 and the EPSRC grant Nr. EP/M00483X/1.","oa":1,"quality_controlled":"1","publisher":"EDP Sciences","year":"2015","publication":"ESAIM: Mathematical Modelling and Numerical Analysis","day":"01","page":"1745 - 1769","date_created":"2018-12-11T11:53:11Z","doi":"10.1051/m2an/2015043","date_published":"2015-11-01T00:00:00Z"},{"quality_controlled":"1","publisher":"Faculté des sciences de Toulouse","oa":1,"year":"2015","day":"01","publication":"Annales de la faculté des sciences de Toulouse","page":"781 - 800","doi":"10.5802/afst.1464","date_published":"2015-01-01T00:00:00Z","date_created":"2018-12-11T11:53:10Z","citation":{"mla":"Erbar, Matthias, et al. “Discrete Ricci Curvature Bounds for Bernoulli-Laplace and Random Transposition Models.” Annales de La Faculté Des Sciences de Toulouse, vol. 24, no. 4, Faculté des sciences de Toulouse, 2015, pp. 781–800, doi:10.5802/afst.1464.","short":"M. Erbar, J. Maas, P. Tetali, Annales de La Faculté Des Sciences de Toulouse 24 (2015) 781–800.","ieee":"M. Erbar, J. Maas, and P. Tetali, “Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models,” Annales de la faculté des sciences de Toulouse, vol. 24, no. 4. Faculté des sciences de Toulouse, pp. 781–800, 2015.","ama":"Erbar M, Maas J, Tetali P. Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models. Annales de la faculté des sciences de Toulouse. 2015;24(4):781-800. doi:10.5802/afst.1464","apa":"Erbar, M., Maas, J., & Tetali, P. (2015). Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models. Annales de La Faculté Des Sciences de Toulouse. Faculté des sciences de Toulouse. https://doi.org/10.5802/afst.1464","chicago":"Erbar, Matthias, Jan Maas, and Prasad Tetali. “Discrete Ricci Curvature Bounds for Bernoulli-Laplace and Random Transposition Models.” Annales de La Faculté Des Sciences de Toulouse. Faculté des sciences de Toulouse, 2015. https://doi.org/10.5802/afst.1464.","ista":"Erbar M, Maas J, Tetali P. 2015. Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models. Annales de la faculté des sciences de Toulouse. 24(4), 781–800."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"5520","author":[{"first_name":"Matthias","full_name":"Erbar, Matthias","last_name":"Erbar"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas"},{"full_name":"Tetali, Prasad","last_name":"Tetali","first_name":"Prasad"}],"article_processing_charge":"No","external_id":{"arxiv":["1409.8605"]},"title":"Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models","abstract":[{"text":"We calculate a Ricci curvature lower bound for some classical examples of random walks, namely, a chain on a slice of the n-dimensional discrete cube (the so-called Bernoulli-Laplace model) and the random transposition shuffle of the symmetric group of permutations on n letters.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1409.8605"}],"month":"01","intvolume":" 24","publication_status":"published","language":[{"iso":"eng"}],"issue":"4","volume":24,"_id":"1635","article_type":"original","type":"journal_article","status":"public","date_updated":"2023-10-18T07:48:28Z","department":[{"_id":"JaMa"}]}]