arXiv Analytics

Sign in

arXiv:math/0505175 [math.PR]AbstractReferencesReviewsResources

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

Radoslaw Adamczak

Published 2005-05-10, updated 2005-07-26Version 2

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.

Comments: Slightly enlarged and updated with respect to the previous version. Some misprints corrected
Categories: math.PR
Subjects: 60E15, 60B11
Related articles: Most relevant | Search more
arXiv:1605.08635 [math.PR] (Published 2016-05-27)
Second Order Concentration via Logarithmic Sobolev Inequalities
arXiv:1703.01765 [math.PR] (Published 2017-03-06)
On the convex Poincaré inequality and weak transportation inequalities
arXiv:1706.09446 [math.PR] (Published 2017-06-28)
On the tightness of Gaussian concentration for convex functions

Links

Toolbox