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

Research paper by Radoslaw Adamczak

Indexed on: 26 Jul '05Published on: 26 Jul '05Published in: Mathematics - Probability



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.