Stability of spectral types for Jacobi matrices under decaying random perturbations

Jonathan Breuer; Yoram Last

doi:10.1016/j.jfa.2006.12.003

Stability of spectral types for Jacobi matrices under decaying random perturbations

Jonathan Breuer^*
, Yoram Last

^*Corresponding author for this work

Einstein Institute of Mathematics

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

7 Scopus citations

Abstract

We study stability of spectral types for semi-infinite self-adjoint tridiagonal matrices under random decaying perturbations. We show that absolutely continuous spectrum associated with bounded eigenfunctions is stable under Hilbert-Schmidt random perturbations. We also obtain some results for singular spectral types.

Original language	English
Pages (from-to)	249-283
Number of pages	35
Journal	Journal of Functional Analysis
Volume	245
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2006.12.003
State	Published - 1 Apr 2007

Bibliographical note

Funding Information:
This research was supported in part by The Israel Science Foundation (Grant No. 188/02) and by Grant No. 2002068 from the United States–Israel Binational Science Foundation (BSF), Jerusalem, Israel.

Keywords

Absolutely continuous spectrum
Decaying potentials
Jacobi matrices
One-dimensional Schrödinger operators
Random potentials
Singular continuous spectrum
Spectral stability

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10.1016/j.jfa.2006.12.003

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abstract = "We study stability of spectral types for semi-infinite self-adjoint tridiagonal matrices under random decaying perturbations. We show that absolutely continuous spectrum associated with bounded eigenfunctions is stable under Hilbert-Schmidt random perturbations. We also obtain some results for singular spectral types.",

keywords = "Absolutely continuous spectrum, Decaying potentials, Jacobi matrices, One-dimensional Schr{\"o}dinger operators, Random potentials, Singular continuous spectrum, Spectral stability",

author = "Jonathan Breuer and Yoram Last",

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AU - Last, Yoram

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AB - We study stability of spectral types for semi-infinite self-adjoint tridiagonal matrices under random decaying perturbations. We show that absolutely continuous spectrum associated with bounded eigenfunctions is stable under Hilbert-Schmidt random perturbations. We also obtain some results for singular spectral types.

KW - Absolutely continuous spectrum

KW - Decaying potentials

KW - Jacobi matrices

KW - One-dimensional Schrödinger operators

KW - Random potentials

KW - Singular continuous spectrum

KW - Spectral stability

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Stability of spectral types for Jacobi matrices under decaying random perturbations

Abstract

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Keywords

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