Ricci curvature bounds for weakly interacting Markov chains

TL;DR

This paper introduces a perturbative approach to establish entropic Ricci curvature bounds for various interacting Markov chains, including spin systems, hard-core models, and random walks on groups.

Contribution

It develops a general perturbative method to derive curvature bounds for complex interacting stochastic systems, extending previous techniques.

Findings

Curvature bounds for Glauber dynamics in spin systems

Application to hard-core models

Results for random walks on groups

Abstract

We establish a general perturbative method to prove entropic Ricci curvature bounds for interacting stochastic particle systems. We apply this method to obtain curvature bounds in several examples, namely: Glauber dynamics for a class of spin systems including the Ising and Curie--Weiss models, a class of hard-core models and random walks on groups induced by a conjugacy invariant set of generators.