CONTRACTIVE COUPLING RATES AND CURVATURE LOWER BOUNDS FOR MARKOV CHAINS

• 成果类型: Article
• 署名作者: Pedrotti, Francesco
• 署名单位: Institute of Science & Technology - Austria
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2113
• 发表日期: 2025
• 页码: 196-250
• 关键词: modified logarithmic sobolev; metric-measure-spaces; RICCI CURVATURE; entropy decay; inequalities

摘要

Contractive coupling rates have been recently introduced by Conforti as a and Poincar & eacute; 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-& Eacute;mery 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.