@article{2ef2079e39b04e89abdae64a0e13687c,
title = "Ricci curvature bounds for weakly interacting Markov chains",
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.",
keywords = "Cayley graph, Hardcore model, Ising model, Markov chain, Modified logarithmic Sobolev inequality, Random walk, Ricci curvature",
author = "Matthias Erbar and Christopher Henderson and Georg Menz and Prasad Tetali",
note = "Funding Information: The authors wish to thank Max Fathi, Jan Maas and Andr? Schlichting for stimulating discussions on this work and related topics. This work originated in discussions that took place at the SQuaRE meetings, Displacement convexity for interacting Markov chains, at the American Institute for Mathematics (AIM), California. The authors wish to thank AIM for the inspiring atmosphere making this collaboration possible. M.E. gratefully acknowledges support by the German Research Foundation through the Collaborative Research Center 1060 The Mathematics of Emergent Effects and the Hausdorff Center for Mathematics. Part of this work was performed within the framework of theLABEX MILYON (ANR-10-LABX-0070) of Universit? de Lyon, within the program Investissements d?Avenir (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). G.M. gratefully acknowledges support by the National Science Foundation under Grant No. DMS-1440140, while he was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2015 semester. P.T. gratefully acknowledges support by the NSF grant DMS-1407657 Publisher Copyright: {\textcopyright} 2017, University of Washington. All rights reserved.",
year = "2017",
doi = "10.1214/17-EJP49",
language = "English (US)",
volume = "22",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",
}