{"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"Preprint","article_processing_charge":"No","corr_author":"1","date_created":"2024-07-31T08:02:16Z","day":"02","publication_status":"submitted","status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2308.00516","open_access":"1"}],"date_published":"2023-08-02T00:00:00Z","language":[{"iso":"eng"}],"publication":"arXiv","_id":"17351","external_id":{"arxiv":["2308.00516"]},"department":[{"_id":"JaMa"}],"type":"preprint","citation":{"ista":"Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2308.00516\">10.48550/arXiv.2308.00516</a>.","mla":"Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2308.00516\">10.48550/arXiv.2308.00516</a>.","ieee":"F. Pedrotti, “Contractive coupling rates and curvature lower bounds for Markov chains,” <i>arXiv</i>. .","apa":"Pedrotti, F. (n.d.). Contractive coupling rates and curvature lower bounds for Markov chains. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2308.00516\">https://doi.org/10.48550/arXiv.2308.00516</a>","short":"F. Pedrotti, ArXiv (n.d.).","chicago":"Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2308.00516\">https://doi.org/10.48550/arXiv.2308.00516</a>.","ama":"Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2308.00516\">10.48550/arXiv.2308.00516</a>"},"author":[{"last_name":"Pedrotti","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","full_name":"Pedrotti, Francesco","first_name":"Francesco"}],"oa":1,"related_material":{"record":[{"id":"17336","relation":"dissertation_contains","status":"for_moderation"}]},"title":"Contractive coupling rates and curvature lower bounds for Markov chains","abstract":[{"text":"Contractive coupling rates have been recently introduced by Conforti as a\r\ntool to establish convex Sobolev inequalities (including modified log-Sobolev\r\nand Poincar\\'{e} inequality) for some classes of Markov chains. In this work,\r\nwe show how contractive coupling rates can also be used to prove stronger\r\ninequalities, in the form of curvature lower bounds for Markov chains and\r\ngeodesic convexity of entropic functionals. We illustrate this in several\r\nexamples discussed by Conforti, where in particular, after appropriately\r\nchoosing a parameter function, we establish positive curvature in the entropic\r\nand (discrete) Bakry--\\'{E}mery sense. In addition, we recall and give\r\nstraightforward generalizations of some notions of coarse Ricci curvature, and\r\nwe discuss some of their properties and relations with the concepts of\r\ncouplings and coupling rates: as an application, we show exponential\r\ncontraction of the $p$-Wasserstein distance for the heat flow in the\r\naforementioned examples.","lang":"eng"}],"doi":"10.48550/arXiv.2308.00516","month":"08","year":"2023","date_updated":"2024-08-02T13:50:27Z"}