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June 2016 Entropic Ricci curvature bounds for discrete interacting systems
Max Fathi, Jan Maas
Ann. Appl. Probab. 26(3): 1774-1806 (June 2016). DOI: 10.1214/15-AAP1133

Abstract

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.

Citation

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Max Fathi. Jan Maas. "Entropic Ricci curvature bounds for discrete interacting systems." Ann. Appl. Probab. 26 (3) 1774 - 1806, June 2016. https://doi.org/10.1214/15-AAP1133

Information

Received: 1 January 2015; Revised: 1 July 2015; Published: June 2016
First available in Project Euclid: 14 June 2016

zbMATH: 1345.60076
MathSciNet: MR3513606
Digital Object Identifier: 10.1214/15-AAP1133

Subjects:
Primary: 60J10, 60K35

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.26 • No. 3 • June 2016
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