[{"day":"22","has_accepted_license":"1","article_processing_charge":"No","citation":{"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.","short":"L. Portinale, Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures, Institute of Science and Technology Austria, 2021.","mla":"Portinale, Lorenzo. Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:10030.","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","ieee":"L. Portinale, “Discrete-to-continuum limits of transport problems and gradient flows in the space of measures,” Institute of Science and Technology Austria, 2021.","ista":"Portinale L. 2021. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. Institute of Science and Technology Austria.","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"},"date_published":"2021-09-22T00:00:00Z","alternative_title":["ISTA Thesis"],"type":"dissertation","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."}],"ddc":["515"],"title":"Discrete-to-continuum limits of transport problems and gradient flows in the space of measures","status":"public","_id":"10030","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Published Version","file":[{"creator":"cchlebak","file_size":3876668,"content_type":"application/x-zip-compressed","access_level":"closed","file_name":"tex_and_pictures.zip","checksum":"8cd60dcb8762e8f21867e21e8001e183","date_created":"2021-09-21T09:17:34Z","date_updated":"2022-03-10T12:14:42Z","file_id":"10032","relation":"source_file"},{"file_name":"thesis_portinale_Final (1).pdf","access_level":"open_access","content_type":"application/pdf","file_size":2532673,"creator":"cchlebak","relation":"main_file","file_id":"10047","date_updated":"2021-09-27T11:14:31Z","date_created":"2021-09-27T11:14:31Z","checksum":"9789e9d967c853c1503ec7f307170279"}],"month":"09","publication_identifier":{"issn":["2663-337X"]},"project":[{"_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","call_identifier":"FWF"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"supervisor":[{"last_name":"Maas","first_name":"Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan"}],"degree_awarded":"PhD","acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"NanoFab"}],"language":[{"iso":"eng"}],"doi":"10.15479/at:ista:10030","file_date_updated":"2022-03-10T12:14:42Z","publication_status":"published","publisher":"Institute of Science and Technology Austria","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"year":"2021","acknowledgement":"The author gratefully acknowledges support by the Austrian Science Fund (FWF), grants No W1245.","date_created":"2021-09-21T09:14:15Z","date_updated":"2023-09-07T13:31:06Z","author":[{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale","first_name":"Lorenzo","full_name":"Portinale, Lorenzo"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"10022"},{"status":"public","relation":"part_of_dissertation","id":"9792"},{"status":"public","relation":"part_of_dissertation","id":"7573"}]}},{"month":"07","language":[{"iso":"eng"}],"doi":"10.48550/arXiv.2106.11217","project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2106.11217"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2106.11217","open_access":"1"}],"ec_funded":1,"article_number":"2106.11217","date_created":"2021-08-06T09:07:12Z","date_updated":"2023-11-14T13:21:01Z","author":[{"full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","last_name":"Feliciangeli","first_name":"Dario"},{"first_name":"Augusto","last_name":"Gerolin","full_name":"Gerolin, Augusto"},{"full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale","first_name":"Lorenzo"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"9733"},{"relation":"dissertation_contains","status":"public","id":"10030"},{"status":"public","relation":"later_version","id":"12911"}]},"publication_status":"submitted","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"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].","year":"2021","day":"21","has_accepted_license":"1","article_processing_charge":"No","date_published":"2021-07-21T00:00:00Z","publication":"arXiv","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.","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” arXiv. .","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","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.","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” ArXiv, 2106.11217, doi:10.48550/arXiv.2106.11217.","short":"D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.)."},"abstract":[{"lang":"eng","text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on careful a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem."}],"type":"preprint","oa_version":"Preprint","title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","ddc":["510"],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9792"},{"has_accepted_license":"1","article_processing_charge":"No","day":"20","date_published":"2021-08-20T00:00:00Z","citation":{"ama":"Feliciangeli D. The polaron at strong coupling. 2021. doi:10.15479/at:ista:9733","ista":"Feliciangeli D. 2021. The polaron at strong coupling. Institute of Science and Technology Austria.","apa":"Feliciangeli, D. (2021). The polaron at strong coupling. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:9733","ieee":"D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and Technology Austria, 2021.","mla":"Feliciangeli, Dario. The Polaron at Strong Coupling. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:9733.","short":"D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and Technology Austria, 2021.","chicago":"Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:9733."},"page":"180","abstract":[{"lang":"eng","text":"This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author."}],"type":"dissertation","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","file":[{"content_type":"application/pdf","file_size":1958710,"creator":"dfelicia","access_level":"open_access","file_name":"Thesis_FeliciangeliA.pdf","checksum":"e88bb8ca43948abe060eb2d2fa719881","date_updated":"2021-09-06T09:28:56Z","date_created":"2021-08-19T14:03:48Z","relation":"main_file","file_id":"9944"},{"access_level":"closed","file_name":"thesis.7z","file_size":3771669,"content_type":"application/octet-stream","creator":"dfelicia","relation":"source_file","file_id":"9945","checksum":"72810843abee83705853505b3f8348aa","date_created":"2021-08-19T14:06:35Z","date_updated":"2022-03-10T12:13:57Z"}],"_id":"9733","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"The polaron at strong coupling","ddc":["515","519","539"],"status":"public","publication_identifier":{"issn":["2663-337X"]},"month":"08","doi":"10.15479/at:ista:9733","language":[{"iso":"eng"}],"supervisor":[{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert"},{"first_name":"Jan","last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan"}],"degree_awarded":"PhD","oa":1,"tmp":{"short":"CC BY-ND (4.0)","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode"},"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"},{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"ec_funded":1,"file_date_updated":"2022-03-10T12:13:57Z","license":"https://creativecommons.org/licenses/by-nd/4.0/","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"9787"},{"id":"9792","relation":"part_of_dissertation","status":"public"},{"id":"9225","relation":"part_of_dissertation","status":"public"},{"id":"9781","status":"public","relation":"part_of_dissertation"},{"id":"9791","status":"public","relation":"part_of_dissertation"}]},"author":[{"orcid":"0000-0003-0754-8530","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","last_name":"Feliciangeli","first_name":"Dario","full_name":"Feliciangeli, Dario"}],"date_created":"2021-07-27T15:48:30Z","date_updated":"2024-03-06T12:30:44Z","year":"2021","department":[{"_id":"GradSch"},{"_id":"RoSe"},{"_id":"JaMa"}],"publisher":"Institute of Science and Technology Austria","publication_status":"published"},{"doi":"10.1007/s10955-019-02434-w","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1811.04572"],"isi":["000498933300001"]},"quality_controlled":"1","isi":1,"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"},{"name":"Taming Complexity in Partial Di erential Systems","call_identifier":"FWF","grant_number":" F06504","_id":"260482E2-B435-11E9-9278-68D0E5697425"}],"month":"01","publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"author":[{"full_name":"Carlen, Eric A.","first_name":"Eric A.","last_name":"Carlen"},{"full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","first_name":"Jan"}],"related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1007/s10955-020-02671-4"}]},"date_created":"2019-04-30T07:34:18Z","date_updated":"2023-08-17T13:49:40Z","volume":178,"year":"2020","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:47:28Z","ec_funded":1,"date_published":"2020-01-01T00:00:00Z","publication":"Journal of Statistical Physics","citation":{"ista":"Carlen EA, Maas J. 2020. Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. Journal of Statistical Physics. 178(2), 319–378.","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","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.","ama":"Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. Journal of Statistical Physics. 2020;178(2):319-378. doi:10.1007/s10955-019-02434-w","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.","mla":"Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems.” Journal of Statistical Physics, vol. 178, no. 2, Springer Nature, 2020, pp. 319–78, doi:10.1007/s10955-019-02434-w.","short":"E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378."},"article_type":"original","page":"319-378","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","file":[{"content_type":"application/pdf","file_size":905538,"creator":"dernst","file_name":"2019_JourStatistPhysics_Carlen.pdf","access_level":"open_access","date_created":"2019-12-23T12:03:09Z","date_updated":"2020-07-14T12:47:28Z","checksum":"7b04befbdc0d4982c0ee945d25d19872","relation":"main_file","file_id":"7209"}],"oa_version":"Published Version","_id":"6358","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["500"],"title":"Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems","status":"public","intvolume":" 178","abstract":[{"lang":"eng","text":"We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates."}],"issue":"2","type":"journal_article"},{"type":"book_chapter","abstract":[{"lang":"eng","text":"We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean space, motivated by the famous theorem of Gromov about the waist of radially symmetric Gaussian measures. In particular, it turns our possible to extend Gromov’s original result to the case of not necessarily radially symmetric Gaussian measure. We also provide examples of measures having no t-neighborhood waist property, including a rather wide class\r\nof compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument to produce some estimates of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures."}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"74","intvolume":" 2256","status":"public","title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","oa_version":"Preprint","scopus_import":"1","series_title":"LNM","article_processing_charge":"No","day":"21","citation":{"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.","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.","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","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.","mla":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer Nature, 2020, pp. 1–27, doi:10.1007/978-3-030-36020-7_1.","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27."},"publication":"Geometric Aspects of Functional Analysis","page":"1-27","date_published":"2020-06-21T00:00:00Z","ec_funded":1,"year":"2020","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"editor":[{"full_name":"Klartag, Bo'az","first_name":"Bo'az","last_name":"Klartag"},{"first_name":"Emanuel","last_name":"Milman","full_name":"Milman, Emanuel"}],"publisher":"Springer Nature","publication_status":"published","author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"volume":2256,"date_created":"2018-12-11T11:44:29Z","date_updated":"2023-08-17T13:48:31Z","publication_identifier":{"eisbn":["9783030360207"],"issn":["00758434"],"eissn":["16179692"],"isbn":["9783030360191"]},"month":"06","main_file_link":[{"url":"https://arxiv.org/abs/1808.07350","open_access":"1"}],"external_id":{"arxiv":["1808.07350"],"isi":["000557689300003"]},"oa":1,"project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1,"doi":"10.1007/978-3-030-36020-7_1","language":[{"iso":"eng"}]}]