99-421 M Krishna, K B Sinha

Spectra of Anderson Type models with decaying randomness (71K, LaTex 2e) Nov 8, 99

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Abstract. In this paper we consider some Anderson Type models with the free parts having long range tails and the random perturbations decaying at different rates in different directions to prove that there is absolutely continuous spectrum in the models which is pure. We also show the existence of purely point spectrum outside some interval. Our models include random potentials decaying in all directions in which case we show the absence of singular continuous spectrum also. We note that our models still have some sort of short range condition on the decay of the potentials in a majority of directions.

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