Weak logarithmic Sobolev inequalities and entropic convergence (2005)
by
P. Cattiaux
,
I. Gentil
,
A. Guillin
| Citations: | 2 - 1 self |
BibTeX
@MISC{Cattiaux05weaklogarithmic,
author = {P. Cattiaux and I. Gentil and A. Guillin},
title = {Weak logarithmic Sobolev inequalities and entropic convergence},
year = {2005}
}
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Abstract
In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré 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 Poincaré inequality can not be used for deriving entropic convergence whence weak logarithmic Sobolev inequality ensures the result.
