Entropic Ricci curvature bounds for discrete interacting systems

TL;DR

This paper introduces a systematic method to establish entropic Ricci curvature lower bounds for Markov chains on discrete sets, unifying previous results and providing new bounds for zero-range processes.

Contribution

The paper presents a general, systematic approach for proving entropic Ricci curvature bounds in discrete Markov chains, covering many known examples and introducing new bounds for zero-range processes.

Findings

Unified method for Ricci curvature bounds in discrete Markov chains

New bounds obtained for zero-range processes on complete graphs

Applicable to various models like birth-death, Bernoulli-Laplace, and random transpositions

Abstract

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.