A Wegner-type Estimate for Correlated Potentials

We propose a fairly simple and natural extension of Stollmann’s lemma to correlated random variables. This extension allows to obtain Wegner-type estimates even in various problems of spectral analysis of random operators where the original Wegner’s lemma is inapplicable, e.g., for correlated random potentials with singular marginal distributions and for multi-particle Hamiltonians.