Jm. Combes et Pd. Hislop, LOCALIZATION FOR SOME CONTINUOUS, RANDOM HAMILTONIANS IN D-DIMENSIONS, Journal of functional analysis, 124(1), 1994, pp. 149-180
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.