Weak logarithmic Sobolev inequalities and entropic convergence
Probability
2007-05-23 v2
Abstract
In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincar\'{e} inequalities, general Beckner inequalities...). We also discuss the quantitative behaviour of relative entropy along a symmetric diffusion semi-group. In particular, we exhibit an example where Poincar\'{e} inequality can not be used for deriving entropic convergence whence weak logarithmic Sobolev inequality ensures the result.
Cite
@article{arxiv.math/0511255,
title = {Weak logarithmic Sobolev inequalities and entropic convergence},
author = {Patrick Cattiaux and Ivan Gentil and Arnaud Guillin},
journal= {arXiv preprint arXiv:math/0511255},
year = {2007}
}