Electronic Journal of Probability
- Electron. J. Probab.
- Volume 22 (2017), paper no. 40, 23 pp.
Ricci curvature bounds for weakly interacting Markov chains
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.
Electron. J. Probab., Volume 22 (2017), paper no. 40, 23 pp.
Received: 23 August 2016
Accepted: 14 March 2017
First available in Project Euclid: 28 April 2017
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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