1Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland 2Institute of Mathematics University of Warsaw Banacha 2 02–097 Warszawa, Poland
Studia Mathematica, Tome 230 (2015) no. 1, pp. 59-93
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 functions 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:
provide mild sufficient condition probability measure real line satisfy modified log sobolev inequality convex functions interpolating between classical log sobolev inequality bobkov ledoux type inequality consequence obtain dimension free two level concentration results convex functions independent random variables sufficiently regular tail decay provide link between modified log sobolev inequalities convex functions weak transport entropy inequalities complementing recent work gozlan roberto samson tetali
Affiliations des auteurs :
Radosław Adamczak
1
;
Michał Strzelecki
2
1
Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland
2
Institute of Mathematics University of Warsaw Banacha 2 02–097 Warszawa, Poland
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title = {Modified {log-Sobolev} inequalities for convex functions on the real line. {Sufficient} conditions},
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Radosław Adamczak; Michał Strzelecki. Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions. Studia Mathematica, Tome 230 (2015) no. 1, pp. 59-93. doi: 10.4064/sm8319-12-2015
