ENTROPIC RICCI CURVATURE BOUNDS FOR DISCRETE INTERACTING SYSTEMS

• 成果类型: Article
• 署名作者: Fathi, Max; Maas, Jan
• 署名单位: Sorbonne Universite; Institute of Science & Technology - Austria
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1133
• 发表日期: 2016
• 页码: 1774-1806
• 关键词: logarithmic sobolev inequalities; metric-measure-spaces; spectral gap; transportation; decay

摘要

We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets. Using different methods, such bounds have recently been obtained in several examples (e.g., 1-dimensional birth and death chains, product chains, Bernoulli-Laplace models, and random transposition models). However, a general method to obtain discrete Ricci bounds had been lacking. Our method covers all of the examples above. In addition, we obtain new Ricci curvature bounds for zero-range processes on the complete graph. The method is inspired by recent work of Caputo, Dai Pra and Posta on discrete functional inequalities.