Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions

Radosław Adamczak; Michał Strzelecki

doi:10.4064/sm8319-12-2015

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arXiv · 1505.05493

Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions

Radosław Adamczak·Michał Strzelecki

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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.

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Radosław Adamczak, Michał Strzelecki. 2015-12-29. Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions. https://doi.org/10.4064/sm8319-12-2015

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