### Abstract

We present a decomposition which highlights the presence of a Bernoulli component in any random variable. Two applications are discussed: 1. A concentration inequality in the spirit of Littlewood-Offord for a class of functions of independent random variables; 2. A proof, based on the Bernoulli case, of spectral localization for random Schroedinger operators with arbitrary probability distributions for the single site coupling constants. (This is joint work with M. Aizenman, F. Germinet and A. Klein)