Modified logarithmic Sobolev inequalities on R
Probability
2007-05-23 v1
Abstract
We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and G\"{o}tze. Under mild assumptions the condition is also necessary. Concentration inequalities are derived. This completes the picture given in recent contributions by Gentil, Guillin and Miclo.
Keywords
Cite
@article{arxiv.math/0612026,
title = {Modified logarithmic Sobolev inequalities on R},
author = {Franck Barthe and Cyril Roberto},
journal= {arXiv preprint arXiv:math/0612026},
year = {2007}
}