Stability of Spectral Types for Jacobi Matrices Under Decaying Random Perturbations

2007/01/10 by Jonathan Breuer, Breuer, Jonathan, Yoram Last +1
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Random Matrices and Applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP

paper · pdf · doi:10.48550/arxiv.math/0701279

arxiv created 2007/01/10 · openalex publication_date 2007/01/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Preservation of the absolutely continuous spectrum of Schrödinger equation under perturbations by slowly decreasing potentials and a.e. convergence of integral operators

Related

• Spectral Properties of Random Non-self-adjoint Matrices and Operators
• Stability of Singular Spectral Types under Decaying Perturbations
• Spectral and Dynamical Properties of Certain Random Jacobi Matrices with Growing Parameters
• Spectral properties of random perturbations of non-normal Toeplitz matrices
• Decay bounds on eigenfunctions and the singular spectrum of unbounded Jacobi matrices