From the Pr\'ekopa-Leindler inequality to modified logarithmic Sobolev inequality
Probability
2007-10-29 v1
Abstract
We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux. Using the Pr\'ekopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on , with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality for all uniform strictly convex potential as well as the Euclidean logarithmic Sobolev inequality.
Keywords
Cite
@article{arxiv.0710.5025,
title = {From the Pr\'ekopa-Leindler inequality to modified logarithmic Sobolev inequality},
author = {Ivan Gentil},
journal= {arXiv preprint arXiv:0710.5025},
year = {2007}
}