Kahane-Khinchin type Averages

Abstract

We prove a Kahane-Khinchin type result with a few random vectors, which are distributed independently with respect to an arbitrary log-concave probability measure on ${\mathbb{R}}^n$. This is an application of small ball estimate and Chernoff's method, that has been recently used in the context of Asymptotic Geometric Analysis in [1], [2].