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Entropic Ricci curvature bounds for discrete interacting systems

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.
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Submitted on : Thursday, September 1, 2016 - 11:14:31 AM
Last modification on : Friday, March 27, 2020 - 4:00:16 AM

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Max Fathi, Jan Maas. Entropic Ricci curvature bounds for discrete interacting systems. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2016, 26 (3), pp.1774-1806. ⟨10.1214/15-AAP1133⟩. ⟨hal-01358648⟩



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