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- W4385958501 abstract "Contractive coupling rates have been recently introduced by Conforti as a tool to establish convex Sobolev inequalities (including modified log-Sobolev and Poincar'{e} inequality) for some classes of Markov chains. In this work, we show how contractive coupling rates can also be used to prove stronger inequalities, in the form of curvature lower bounds for Markov chains and geodesic convexity of entropic functionals. We illustrate this in several examples discussed by Conforti, where in particular, after appropriately choosing a parameter function, we establish positive curvature in the entropic and (discrete) Bakry--'{E}mery sense. In addition, we recall and give straightforward generalizations of some notions of coarse Ricci curvature, and we discuss some of their properties and relations with the concepts of couplings and coupling rates: as an application, we show exponential contraction of the $p$-Wasserstein distance for the heat flow in the aforementioned examples." @default.
- W4385958501 created "2023-08-18" @default.
- W4385958501 creator A5008315500 @default.
- W4385958501 date "2023-08-01" @default.
- W4385958501 modified "2023-09-23" @default.
- W4385958501 title "Contractive coupling rates and curvature lower bounds for Markov chains" @default.
- W4385958501 doi "https://doi.org/10.48550/arxiv.2308.00516" @default.
- W4385958501 hasPublicationYear "2023" @default.
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