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.
Cite this article
Naomasa Ueki, Wegner Estimates and Localization for Gaussian Random Potentials. Publ. Res. Inst. Math. Sci. 40 (2004), no. 1, pp. 29–90DOI 10.2977/PRIMS/1145475966