Spectral and dynamical properties of certain random Jacobi matrices with growing parameters

DOI10.1090/S0002-9947-10-04856-7zbMath1192.47027arXiv0708.0670MaRDI QIDQ3566711

Jonathan Breuer

Publication date: 8 June 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.0670

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (8)

About essential spectra of unbounded Jacobi matrices ⋮ Level repulsion for Schrödinger operators with singular continuous spectrum ⋮ Orthogonal polynomials with recursion coefficients of generalized bounded variation ⋮ Eigenvalue spacings and dynamical upper bounds for discrete one-dimensional Schrödinger operators ⋮ The Nevai condition ⋮ Generalized Prüfer variables for perturbations of Jacobi and CMV matrices ⋮ Spectral fluctuations for Schrödinger operators with a random decaying potential ⋮ Dimension results for the spectral measure of the circular \(\beta\) ensembles

Cites Work

• Some Jacobi matrices with decaying potential and dense point spectrum
• Eigenvalue statistics for CMV matrices: From Poisson to clock via random matrix ensembles
• Appearance of a purely singular continuous spectrum in a class of random Schrödinger operators
• One-dimensional Schrödinger operators with random decaying potentials
• On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
• Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators
• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators
• Power-law subordinacy and singular spectra. I: Half-line operators
• Spectral analysis of selfadjoint Jacobi matrices with periodically modulated entries
• Solutions, spectrum, and dynamics for Schrödinger operators on infinite domains
• Quantum dynamics and decompositions of singular continuous spectra
• Random discrete Schrödinger operators from random matrix theory
• Matrix models for beta ensembles
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