LOCALIZATION FOR SOME CONTINUOUS, RANDOM HAMILTONIANS IN D-DIMENSIONS

We prove the existence with probability one of an interval of pure poi nt spectrum for some families of continuous random Schrodinger operato rs in d-dimensions. For Anderson-like models with positive, short-rang e, single-site potentials, we also prove that the corresponding eigenf unctions decay exponentially and that the integrated density of states is Lipschitz continuous. For the other families of random potentials that we study, we show that the corresponding eigenfunctions decay fas ter than an inverse power of x, which depends upon the decay rate of t he single-site potential. To obtain these results, we develop an exten sion of the classical Aronszajn-Donoghue theory for a class of relativ ely compact perturbations and a spectral averaging method which extend s Kotani's trick to these more general families of operators. (C) 1994 Academic Press, Inc.