Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses

Radoslaw Adamczak

Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses

Probability 2007-05-23 v2

Authors: Radoslaw Adamczak

Abstract

We prove logarithmic Sobolev inequalities and concentration results for convex functions and a class of product random vectors. The results are used to derive tail and moment inequalities for chaos variables (in spirit of Talagrand and Arcones, Gine). We also show that the same proof may be used for chaoses generated by log-concave random variables, recovering results by Lochowski and present an application to exponential integrability of Rademacher chaos.

Keywords

logarithmic sobolev inequality concentration of measure convex function polynomial chaos log-concave random variable rademacher chaos tail inequality

Cite

@article{arxiv.math/0505175,
  title  = {Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses},
  author = {Radoslaw Adamczak},
  journal= {arXiv preprint arXiv:math/0505175},
  year   = {2007}
}

Comments

Slightly enlarged and updated with respect to the previous version. Some misprints corrected

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