English

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}
}