Some abstract Wegner estimates with applications

Mostafa Sabri

Published 2012-12-09, updated 2013-07-18Version 2

We prove some abstract Wegner bounds for random self-adjoint operators. Applications include elementary proofs of Wegner estimates for discrete and continuous Anderson Hamiltonians with possibly sparse potentials, as well as Wegner bounds for quantum graphs with random edge length or random vertex coupling. We allow the coupling constants describing the randomness to be correlated and to have quite general distributions.