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Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions
- Source :
- Studia Math. 230 (2015), 59-93
- Publication Year :
- 2015
-
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.<br />Comment: 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
- Subjects :
- Mathematics - Probability
60E15 (Primary), 26A51, 26B25, 26D10 (Secondary)
Subjects
Details
- Database :
- arXiv
- Journal :
- Studia Math. 230 (2015), 59-93
- Publication Type :
- Report
- Accession number :
- edsarx.1505.05493
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.4064/sm8319-12-2015