Wegner Estimates and Localization for Gaussian Random Potentials

Abstract

A Wegner estimate is proven for a Schr¨dinger operator with a bounded random o vector potential and a Gaussian random scalar potential. The estimate is used to prove the strong dynamical localization and the exponential decay of the eigenfunctions. For the proof, Klopp’s method using a vector field on a probability space and Germinet and Klein’s bootstrap multiscale analysis are applied. Moreover Germinet and Klein’s characterization of the Anderson metal-insulator transport transition is extended to the above operator.