Open Access
2017 Ricci curvature bounds for weakly interacting Markov chains
Matthias Erbar, Christopher Henderson, Georg Menz, Prasad Tetali
Electron. J. Probab. 22: 1-23 (2017). DOI: 10.1214/17-EJP49


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.


Download Citation

Matthias Erbar. Christopher Henderson. Georg Menz. Prasad Tetali. "Ricci curvature bounds for weakly interacting Markov chains." Electron. J. Probab. 22 1 - 23, 2017.


Received: 23 August 2016; Accepted: 14 March 2017; Published: 2017
First available in Project Euclid: 28 April 2017

zbMATH: 1362.60084
MathSciNet: MR3646066
Digital Object Identifier: 10.1214/17-EJP49

Primary: 60B15 , 60J22 , 60K35

Keywords: Cayley graph , hardcore model , Ising model , Markov chain , Modified logarithmic Sobolev inequality , Random walk , Ricci curvature

Vol.22 • 2017
Back to Top