Stability of spectral types for Jacobi matrices under decaying random perturbations

Jonathan Breuer*, Yoram Last

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Pages (from-to)249-283
Number of pages35
JournalJournal of Functional Analysis
Volume245
Issue number1
DOIs
StatePublished - 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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