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

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

2007-05-11

arxiv.org/abs/0705.1707v2

Physics

Mathematical Physics

7 pages, typos corrected in v2, to appear in Proc. Amer. Math. Soc

Scientific paper

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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