Poincar\'e, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature

摘要

We study functional inequalities for Markov chains on discrete spaces withentropic Ricci curvature bounded from below. Our main results are that whencurvature is non-negative, but not necessarily positive, the spectral gap, theCheeger isoperimetric constant and the modified logarithmic Sobolev constant ofthe chain can be bounded from below by a constant that only depends on thediameter of the space, with respect to a suitable metric. These estimates arediscrete analogues of classical results of Riemannian geometry obtained by Liand Yau, Buser and Wang.