On talagrand’s deviation inequalities for product measures

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 these 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. © 1996 Société de Mathématiques Appliquées et Industrielles.