Peter D. Hislop and Peter Mueller
A lower bound for the density of states of the lattice Anderson model
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ABSTRACT. We consider the Anderson model on the lattice $\mathbb{Z}^{d}$ 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 density with compact support, and if the Lebesgue density is
essentially bounded away from zero on its support, then we prove
that the density of states is strictly positive Lebesgue almost
every energy in the deterministic spectrum.