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

• Autorzy: Radosław Adamczak , Michał Strzelecki
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 26B25: Convexity, generalizations
• 26A51: Convexity, generalizations
• 60E15: Inequalities; stochastic orderings
• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 230
• Numer: 1
• Strony: 59-93

Daty

wydano

2015

Twórcy

autor

Radosław Adamczak

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

autor

Michał Strzelecki

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/sm8319-12-2015