Modified log-Sobolev inequalities for strongly log-concave distributions

03/14/2019

∙

by   Mary Cryan, et al.

∙

0

∙

share

We show that the modified log-Sobolev constant for a natural Markov chain which converges to an r-homogeneous strongly log-concave distribution is at least 1/r. As a consequence, we obtain an asymptotically optimal mixing time bound for this chain. Applications include the bases-exchange random walk in a matroid.