Local Wegner and Minami estimates for continuous random Schrödinger operators

Details Local Wegner and Minami estimates for continuous random Schrödinger operators Local Wegner and Minami estimates for continuous random Schrödinger operators

2011-11-20

arxiv.org/abs/1111.4674v1

Physics

Mathematical Physics

Scientific paper

We introduce and prove local Wegner estimates for continuous generalized Anderson Hamiltonians, where the single-site random variables are independent but not necessarily identically distributed. We use them to prove Minami's estimate for continuous Anderson Hamiltonians whose single site probability distribution has a bounded density and satisfy a simple covering condition. Eigenvalues statistics such as Poisson statistics and level spacings statistics follow for such continuous Anderson Hamiltonians, as well as simplicity of eigenvalues. As another application of local Wegner estimates, we show that the (differentiated) density of states exhibits the same Lifshitz tails upper bound as the integrated density of states.

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