The Annals of Applied Probability

Entropic Ricci curvature bounds for discrete interacting systems

Max Fathi and Jan Maas

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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.

Article information

Ann. Appl. Probab., Volume 26, Number 3 (2016), 1774-1806.

Received: January 2015
Revised: July 2015
First available in Project Euclid: 14 June 2016

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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]

Discrete Ricci curvature transport metrics functional inequalities birth-death processes zero-range processes Bernoulli–Laplace model random transposition model


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.

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