A sharp log-Sobolev inequality for the multislice
Probability
2020-04-14 v1 Discrete Mathematics
Combinatorics
Abstract
We determine the log-Sobolev constant of the multi-urn Bernoulli-Laplace diffusion model with arbitrary parameters, up to a small universal multiplicative constant. Our result extends a classical estimate of Lee and Yau (1998) and confirms a conjecture of Filmus, O'Donnell and Wu (2018). Among other applications, we completely quantify the "small-set expansion" phenomenon on the multislice, and obtain sharp mixing-time estimates for the colored exclusion process on various graphs.
Keywords
Cite
@article{arxiv.2004.05833,
title = {A sharp log-Sobolev inequality for the multislice},
author = {Justin Salez},
journal= {arXiv preprint arXiv:2004.05833},
year = {2020}
}
Comments
23 pages, comments welcome