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


Authors: Peter D. Hislop and Peter Müller
Journal: Proc. Amer. Math. Soc. 136 (2008), 2887-2893
MSC (2000): Primary 47B80, 35P15, 81Q10
DOI: https://doi.org/10.1090/S0002-9939-08-09361-1
Published electronically: April 14, 2008
MathSciNet review: 2399055
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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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Additional Information

Peter D. Hislop
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
Email: hislop@ms.uky.edu

Peter Müller
Affiliation: Institut für Theoretische Physik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
Address at time of publication: Mathematisches Institut Ludwig-Maximilians-Universität, Theresienstr. 39, 80333, München, Germany
Email: peter.mueller@physik.uni-goe.de

DOI: https://doi.org/10.1090/S0002-9939-08-09361-1
Keywords: Random Schr\"odinger operators, integrated density of states, Wegner estimate, lower bound
Received by editor(s): May 11, 2007
Published electronically: April 14, 2008
Dedicated: Dedicated to Jean-Michel Combes on the occasion of his 65$^{th}$ birthday
Communicated by: Walter Craig
Article copyright: © Copyright 2008 American Mathematical Society

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