Log-Sobolev, isoperimetry and transport inequalities on graphs
Probability
2015-05-19 v1
Abstract
In this paper, we study some functional inequalities (such as Poincar\'e inequalities, logarithmic Sobolev inequalities, generalized Cheeger isoperimetric inequalities, transportation-information inequalities and transportation-entropy inequalities) for reversible nearest-neighbor Markov processes on a connected finite graph by means of (random) path method. We provide estimates of the involved constants.
Keywords
Cite
@article{arxiv.1505.04552,
title = {Log-Sobolev, isoperimetry and transport inequalities on graphs},
author = {Yutao Ma and Ran Wang and Liming Wu},
journal= {arXiv preprint arXiv:1505.04552},
year = {2015}
}