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arXiv · 1602.05414

Ricci curvature bounds for weakly interacting Markov chains

Matthias Erbar·Christopher Henderson·Georg Menz·Prasad Tetali
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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.

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Matthias Erbar, Christopher Henderson, Georg Menz, Prasad Tetali. 2016-02-17. Ricci curvature bounds for weakly interacting Markov chains. https://arxiv.org/abs/1602.05414

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