Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions
Abstract
We provide a mild sufficient condition for a probability measure on the real line to satisfy a modified log-Sobolev inequality for convex functions, interpolating between the classical log-Sobolev inequality and a Bobkov-Ledoux type inequality. As a consequence we obtain dimension-free two-level concentration results for convex function of independent random variables with sufficiently regular tail decay. We also provide a link between modified log-Sobolev inequalities for convex functions and weak transport-entropy inequalities, complementing recent work by Gozlan, Roberto, Samson, and Tetali.
Keywords
Cite
@article{arxiv.1505.05493,
title = {Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions},
author = {Radosław Adamczak and Michał Strzelecki},
journal= {arXiv preprint arXiv:1505.05493},
year = {2016}
}
Comments
25 pages; changes: references and comments about recent results by other Authors added, hypercontractive estimates in Section 3 added, a few typos corrected; accepted for publication in Studia Mathematica