Poincar{\'e} and logarithmic sobolev inequalities for nearly radial measures
Functional Analysis
2019-12-24 v1 Probability
Abstract
If Poincar{\'e} inequality has been studied by Bobkov for radial measures, few is known about the logarithmic Sobolev inequalty in the radial case. We try to fill this gap here using different methods: Bobkov's argument and super-Poincar{\'e} inequalities, direct approach via L1-logarithmic Sobolev inequalities. We also give various examples where the obtained bounds are quite sharp. Recent bounds obtained by Lee-Vempala in the logconcave bounded case are refined for radial measures.
Keywords
Cite
@article{arxiv.1912.10825,
title = {Poincar{\'e} and logarithmic sobolev inequalities for nearly radial measures},
author = {Patrick Cattiaux and Arnaud Guillin and Liming Wu},
journal= {arXiv preprint arXiv:1912.10825},
year = {2019}
}