Wegner estimates and Anderson localization for alloy-type potentials
This paper proves a Wegner estimate for random Schrödinger operators on \(L^2(\mathbb{R}^d)\). This estimate is one of the main ingredients to prove Anderson localization via the multiscale analysis technique. The random potential considered is given by \(V_w(x)=q_i(w)f(x-i)\), where \(q_i\) are i.i.d. random variables with common distribution \(g(\lambda)d\lambda\). \(f\) is supposed to be nonnegative and strictly positive on an open set.
scientific article; zbMATH DE number 922491