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15 May 2006 Simplicity of singular spectrum in Anderson-type Hamiltonians
Vojkan Jakšić, Yoram Last
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Duke Math. J. 133(1): 185-204 (15 May 2006). DOI: 10.1215/S0012-7094-06-13316-1

Abstract

We study self-adjoint operators of the form Hω=H0+ω(n)(δn|·)δn, where the δn's are a family of orthonormal vectors and the ω(n)'s are independent random variables with absolutely continuous probability distributions. We prove a general structural theorem that provides in this setting a natural decomposition of the Hilbert space as a direct sum of mutually orthogonal closed subspaces, which are a.s. invariant under Hω, and that is helpful for the spectral analysis of such operators. We then use this decomposition to prove that the singular spectrum of Hω is a.s. simple

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Vojkan Jakšić. Yoram Last. "Simplicity of singular spectrum in Anderson-type Hamiltonians." Duke Math. J. 133 (1) 185 - 204, 15 May 2006. https://doi.org/10.1215/S0012-7094-06-13316-1

Information

Published: 15 May 2006
First available in Project Euclid: 19 April 2006

zbMATH: 1107.47027
MathSciNet: MR2219273
Digital Object Identifier: 10.1215/S0012-7094-06-13316-1

Subjects:
Primary: 47B80
Secondary: 47A10, 47B25, 60H25, 81Q10, 82B44

Rights: Copyright © 2006 Duke University Press

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Vol.133 • No. 1 • 15 May 2006
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