Year: 2025
Type: article
Abstract: Contractive coupling rates have been recently introduced by Conforti as a tool to establish convex Sobolev inequalities (including modified log-Sobolev and Poincaré inequality) for some classes of Markov chains. In this work, for most of the examples discussed by Conforti, we use contractive coupling rates to prove stronger inequalities, in the form of curvature lower bounds (in entropic and discrete Bakry–Émery sense) and geodesic convexity of some entropic functionals. 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.
DOI: 10.1214/24-aap2113
Author: Francesco Pedrotti
Institution: Institute of Science and Technology Austria
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408006995