On the joint distribution of energy levels of random Schrödinger operators

Michael Aizenman; Simone Warzel

doi:10.1088/1751-8113/42/4/045201

On the joint distribution of energy levels of random Schrödinger operators

Michael Aizenman, Simone Warzel

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We consider operators with random potentials on graphs, such as the lattice version of the random Schrödinger operator. The main result is a general bound on the probabilities of simultaneous occurrence of eigenvalues in specified distinct intervals, with the corresponding eigenfunctions being separately localized within prescribed regions. The bound generalizes the Wegner estimate on the density of states. The analysis proceeds through a new multi-parameter spectral averaging principle.

Original language	English (US)
Article number	045201
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	42
Issue number	4
DOIs	https://doi.org/10.1088/1751-8113/42/4/045201
State	Published - 2009

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability
Modeling and Simulation
Mathematical Physics
Physics and Astronomy(all)

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10.1088/1751-8113/42/4/045201

Cite this

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abstract = "We consider operators with random potentials on graphs, such as the lattice version of the random Schr{\"o}dinger operator. The main result is a general bound on the probabilities of simultaneous occurrence of eigenvalues in specified distinct intervals, with the corresponding eigenfunctions being separately localized within prescribed regions. The bound generalizes the Wegner estimate on the density of states. The analysis proceeds through a new multi-parameter spectral averaging principle.",

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AB - We consider operators with random potentials on graphs, such as the lattice version of the random Schrödinger operator. The main result is a general bound on the probabilities of simultaneous occurrence of eigenvalues in specified distinct intervals, with the corresponding eigenfunctions being separately localized within prescribed regions. The bound generalizes the Wegner estimate on the density of states. The analysis proceeds through a new multi-parameter spectral averaging principle.

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M3 - Article

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ER -

On the joint distribution of energy levels of random Schrödinger operators

Abstract

All Science Journal Classification (ASJC) codes

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