Dirk Buschmann, G\"unter Stolz
Two-Parameter Spectral Averaging and Localization for Non-Monotoneous 
Random Schr\"odinger Operators
(70K, LaTeX)

ABSTRACT.  We prove exponential localization at all energies for two types of 
one-dimensional random Schr\"odinger operators: the Poisson model 
and the random displacement model. As opposed to Anderson-type 
models, these operators are not monotoneous in the random 
parameters. Therefore the classical one-parameter version of 
spectral averaging, as used in localization proofs for Anderson 
models, breaks down. We use the new method of two-parameter 
spectral averaging and apply it to the Poisson as well as the 
displacement case. In addition, we apply results from inverse 
spectral theory, which show that two-parameter spectral averaging 
works for sufficiently many energies (all but a discrete set) to 
conclude localization at all energies.