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15 July 2002 Localization for one-dimensional, continuum, Bernoulli-Anderson models
David Damanik, Robert Sims, Günter Stolz
Duke Math. J. 114(1): 59-100 (15 July 2002). DOI: 10.1215/S0012-7094-02-11414-8

Abstract

We use scattering theoretic methods to prove strong dynamical and exponential localization for one-dimensional, continuum, Anderson-type models with singular distributions; in particular, the case of a Bernoulli distribution is covered. The operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms. Our main tools are the reflection and transmission coefficients for compactly supported single-site perturbations of a periodic background which we use to verify the necessary hypotheses of multi-scale analysis. We show that nonreflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs.

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David Damanik. Robert Sims. Günter Stolz. "Localization for one-dimensional, continuum, Bernoulli-Anderson models." Duke Math. J. 114 (1) 59 - 100, 15 July 2002. https://doi.org/10.1215/S0012-7094-02-11414-8

Information

Published: 15 July 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1107.82025
MathSciNet: MR1915036
Digital Object Identifier: 10.1215/S0012-7094-02-11414-8

Subjects:
Primary: 82B44
Secondary: 34L40, 47B80

Rights: Copyright © 2002 Duke University Press

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Vol.114 • No. 1 • 15 July 2002
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