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arXiv · 1501.00562

Entropic Ricci curvature bounds for discrete interacting systems

Max Fathi·Jan Maas
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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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Max Fathi, Jan Maas. 2016-06-27. Entropic Ricci curvature bounds for discrete interacting systems. https://doi.org/10.1214/15-aap1133

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