A lower bound for the density of states of the lattice Anderson model

Hislop, Peter; Müller, Peter

doi:10.1090/S0002-9939-08-09361-1

A lower bound for the density of states of the lattice Anderson model
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by Peter D. Hislop and Peter Müller

Proc. Amer. Math. Soc. 136 (2008), 2887-2893

DOI: https://doi.org/10.1090/S0002-9939-08-09361-1

Published electronically: April 14, 2008

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Abstract:

We consider the Anderson model on the multi-dimensional cubic lattice and prove a positive lower bound on the density of states under certain conditions. For example, if the random variables are independently and identically distributed and the probability measure has a bounded Lebesgue density with compact support, and if this density is essentially bounded away from zero on its support, then we prove that the density of states is strictly positive for Lebesgue-almost every energy in the deterministic spectrum.

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