Spectral and Dynamical Properties of Certain Random Jacobi Matrices with Growing Parameters

2007/08/05 by Jonathan Breuer, Breuer, Jonathan · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Random Matrices and Applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP

paper · pdf · doi:10.48550/arxiv.0708.0670

26 pages, some typos corrected and some remarks added

openalex publication_date 2007/08/05 · arxiv created 2008/06/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, a family of random Jacobi matrices, with off-diagonal terms that exhibit power-law growth, is studied. Since the growth of the randomness is slower than that of these terms, it is possible to use methods applied in the study of Schrödinger operators with random decaying potentials. A particular result of the analysis is the existence of operators with arbitrarily fast transport whose spectral measure is zero dimensional. The results are applied to the infinite Gaussian β Ensembles and their spectral properties are analyzed.

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• Decay bounds on eigenfunctions and the singular spectrum of unbounded Jacobi matrices

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