The Annals of Probability

Concentration around the mean for maxima of empirical processes

T. Klein and E. Rio

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In this paper we give optimal constants in Talagrand’s concentration inequalities for maxima of empirical processes associated to independent and eventually nonidentically distributed random variables. Our approach is based on the entropy method introduced by Ledoux.

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Ann. Probab., Volume 33, Number 3 (2005), 1060-1077.

First available in Project Euclid: 6 May 2005

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Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings 60F10: Large deviations

Empirical processes Rademacher processes Talagrand’s inequality tensorization of entropy moderate deviations Bennett’s inequality concentration around the mean


Klein, T.; Rio, E. Concentration around the mean for maxima of empirical processes. Ann. Probab. 33 (2005), no. 3, 1060--1077. doi:10.1214/009117905000000044.

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