- 99-259 G\"unter Stolz
- Non-Monotoneous Random Schr\"odinger Operators: The Anderson Model
(388K, Postscript)
Jul 7, 99
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Abstract. We prove exponential localization at all energies for one-dimensional
continuous Anderson-type models with single site potentials of
changing sign. A periodic background potential is allowed. The main
problem arises from non-monotonicity, i.e. the operator does not
depend monotoneously in form sense on the random parameters. We show
that the method of ``two-parameter spectral averaging'', recently
devised by Buschmann and Stolz to prove localization for Poisson
and random displacement models, can be modified to work for the
type of Anderson model considered here.
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