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On Talagrand's deviation inequalities for product measures

Published online by Cambridge University Press:  15 August 2002

Michel Ledoux
Michel Ledoux*
Affiliation:
Département de Mathéematiques, Laboratoire de Statistique et Probabilités associé au C.N.R.S., Université Paul-Sabatier, 118, route de Narbonne,31062 Toulouse Cedex, France. E-mail : [email protected]
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Abstract

We present a new and simple approach to some of the deviation inequalities for product measures deeply investigated by M. Talagrand in the recent years. Our method is based on functional inequalities of Poincaré and logarithmic Sobolev type and iteration of these inequalities. In particular, we establish with theses tools sharp deviation inequalities from the mean on norms of sums of independent random vectors and empirical processes. Concentration for the Hamming distance may also be deduced from this approach.

Keywords

Concentration of measure / logarithmic Sobolev inequalities / product measures / deviation inequalities / convex functions / bounds on empirical processes.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 1 , 1997 , pp. 63 - 87
Copyright
© EDP Sciences, SMAI, 1997

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