{"year":"2024","abstract":[{"lang":"eng","text":"We study a random matching problem on closed compact  2 -dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers  n  and  m=m(n)  of points, asymptotically equivalent as  n  goes to infinity, the optimal transport plan between the two empirical measures  μn  and  νm  is quantitatively well-approximated by  (Id,exp(∇hn))#μn  where  hn  solves a linear elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère equation. This is obtained in the case of samples of correlated random points for which a stretched exponential decay of the  α -mixing coefficient holds and for a class of discrete-time Markov chains having a unique absolutely continuous invariant measure with respect to the volume measure."}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00440-023-01254-0"}],"author":[{"id":"fea1b376-906f-11eb-847d-b2c0cf46455b","full_name":"Clozeau, Nicolas","last_name":"Clozeau","first_name":"Nicolas"},{"last_name":"Mattesini","first_name":"Francesco","full_name":"Mattesini, Francesco"}],"day":"04","language":[{"iso":"eng"}],"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"},"has_accepted_license":"1","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"ddc":["510"],"title":"Annealed quantitative estimates for the quadratic 2D-discrete random matching problem","citation":{"mla":"Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00440-023-01254-0\">10.1007/s00440-023-01254-0</a>.","ista":"Clozeau N, Mattesini F. 2024. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields.","ieee":"N. Clozeau and F. Mattesini, “Annealed quantitative estimates for the quadratic 2D-discrete random matching problem,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2024.","short":"N. Clozeau, F. Mattesini, Probability Theory and Related Fields (2024).","chicago":"Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00440-023-01254-0\">https://doi.org/10.1007/s00440-023-01254-0</a>.","ama":"Clozeau N, Mattesini F. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. <i>Probability Theory and Related Fields</i>. 2024. doi:<a href=\"https://doi.org/10.1007/s00440-023-01254-0\">10.1007/s00440-023-01254-0</a>","apa":"Clozeau, N., &#38; Mattesini, F. (2024). Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-023-01254-0\">https://doi.org/10.1007/s00440-023-01254-0</a>"},"article_processing_charge":"Yes (in subscription journal)","scopus_import":"1","date_published":"2024-01-04T00:00:00Z","quality_controlled":"1","external_id":{"arxiv":["2303.00353"]},"publisher":"Springer Nature","publication_status":"epub_ahead","date_created":"2024-01-14T23:00:57Z","month":"01","publication":"Probability Theory and Related Fields","type":"journal_article","date_updated":"2024-01-17T11:18:34Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","grant_number":"948819"}],"department":[{"_id":"JuFi"}],"doi":"10.1007/s00440-023-01254-0","oa_version":"Published Version","ec_funded":1,"acknowledgement":"NC has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No 948819).\r\nFM is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the SPP 2265 Random Geometric Systems. FM has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044 -390685587, Mathematics Münster: Dynamics–Geometry–Structure. FM has been funded by the Max Planck Institute for Mathematics in the Sciences.","_id":"14797","article_type":"original","status":"public"}