Electronic Journal of Probability

Ricci curvature bounds for weakly interacting Markov chains

Matthias Erbar, Christopher Henderson, Georg Menz, and Prasad Tetali

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 40, 23 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1493345027

Digital Object Identifier
doi:10.1214/17-EJP49

Mathematical Reviews number (MathSciNet)
MR3646066

Zentralblatt MATH identifier
1362.60084

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J22: Computational methods in Markov chains [See also 65C40] 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization

Keywords
Ricci curvature modified logarithmic Sobolev inequality Markov chain Ising model hardcore model random walk Cayley graph

Rights
Creative Commons Attribution 4.0 International License.

Citation

Erbar, Matthias; Henderson, Christopher; Menz, Georg; Tetali, Prasad. Ricci curvature bounds for weakly interacting Markov chains. Electron. J. Probab. 22 (2017), paper no. 40, 23 pp. doi:10.1214/17-EJP49. https://projecteuclid.org/euclid.ejp/1493345027


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