Stability of spectral types for Jacobi matrices under decaying random perturbations

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• 作者：Jonathan Breuer ; Yoram Last
• 关键词：Spectral stability ; Absolutely continuous spectrum ; Singular continuous spectrum ; Random potentials ; Decaying potentials ; One-dimensional Schrö ; dinger operators ; Jacobi matrices
• 刊名：Journal of Functional Analysis
• 出版年：2007
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：1 April 2007
• 卷：245
• 期：1
• 页码：249-283
• 文件大小：266 K

摘要

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.