Wegner estimate for discrete alloy-type models

Details Wegner estimate for discrete alloy-type models Wegner estimate for discrete alloy-type models

2010-06-25

arxiv.org/abs/1006.4995v1

Mathematics

Spectral Theory

Accepted for publication in AHP. For an earlier version see http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=09-100

Scientific paper

We study discrete alloy-type random Schr\"odinger operators on $\ell^2(\mathbb{Z}^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the single site potential is compactly supported and the distribution of the coupling constant is of bounded variation a Wegner estimate holds. The bound is polynomial in the volume of the box and thus applicable as an ingredient for a localisation proof via multiscale analysis.

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