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

Radosław Adamczak; Michał Strzelecki

Studia Mathematica (2015)

  • Volume: 230, Issue: 1, page 59-93
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Radosław Adamczak, and Michał Strzelecki. "Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions." Studia Mathematica 230.1 (2015): 59-93. <http://eudml.org/doc/285883>.

@article{RadosławAdamczak2015,
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 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. },
author = {Radosław Adamczak, Michał Strzelecki},
journal = {Studia Mathematica},
keywords = {concentration of measure; convex functions; logarithmic Sobolev inequalities},
language = {eng},
number = {1},
pages = {59-93},
title = {Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions},
url = {http://eudml.org/doc/285883},
volume = {230},
year = {2015},
}

TY - JOUR
AU - Radosław Adamczak
AU - Michał Strzelecki
TI - Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions
JO - Studia Mathematica
PY - 2015
VL - 230
IS - 1
SP - 59
EP - 93
AB - 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.
LA - eng
KW - concentration of measure; convex functions; logarithmic Sobolev inequalities
UR - http://eudml.org/doc/285883
ER -

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