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2010 Poisson statistics for eigenvalues of continuum random Schrödinger operators
Jean-Michel Combes, François Germinet, Abel Klein
Anal. PDE 3(1): 49-80 (2010). DOI: 10.2140/apde.2010.3.49

Abstract

We show absence of energy levels repulsion for the eigenvalues of random Schrödinger operators in the continuum. We prove that, in the localization region at the bottom of the spectrum, the properly rescaled eigenvalues of a continuum Anderson Hamiltonian are distributed as a Poisson point process with intensity measure given by the density of states. In addition, we prove that in this localization region the eigenvalues are simple.

These results rely on a Minami estimate for continuum Anderson Hamiltonians. We also give a simple, transparent proof of Minami’s estimate for the (discrete) Anderson model.

Citation

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Jean-Michel Combes. François Germinet. Abel Klein. "Poisson statistics for eigenvalues of continuum random Schrödinger operators." Anal. PDE 3 (1) 49 - 80, 2010. https://doi.org/10.2140/apde.2010.3.49

Information

Received: 9 July 2009; Accepted: 6 August 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1227.82034
MathSciNet: MR2663411
Digital Object Identifier: 10.2140/apde.2010.3.49

Subjects:
Primary: 82B44
Secondary: 47B80, 60H25

Rights: Copyright © 2010 Mathematical Sciences Publishers

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