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.
Cite
@article{arxiv.1501.00562,
title = {Entropic Ricci curvature bounds for discrete interacting systems},
author = {Max Fathi and Jan Maas},
journal= {arXiv preprint arXiv:1501.00562},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.1214/15-AAP1133 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)