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Logarithmic Sobolev inequalities and concentration of measure for convex functions and polynomial chaoses

Adamczak R.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 2

221-238

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 the 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 Łochowski, and present an application to exponential integrability of Rademacher chaos.