The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 3 (2016), 1774-1806.
Entropic Ricci curvature bounds for discrete interacting systems
We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets. Using different methods, such bounds have recently been obtained in several examples (e.g., 1-dimensional birth and death chains, product chains, Bernoulli–Laplace models, and random transposition models). However, a general method to obtain discrete Ricci bounds had been lacking. Our method covers all of the examples above. In addition, we obtain new Ricci curvature bounds for zero-range processes on the complete graph. The method is inspired by recent work of Caputo, Dai Pra and Posta on discrete functional inequalities.
Ann. Appl. Probab., Volume 26, Number 3 (2016), 1774-1806.
Received: January 2015
Revised: July 2015
First available in Project Euclid: 14 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Fathi, Max; Maas, Jan. Entropic Ricci curvature bounds for discrete interacting systems. Ann. Appl. Probab. 26 (2016), no. 3, 1774--1806. doi:10.1214/15-AAP1133. https://projecteuclid.org/euclid.aoap/1465905019