Localization in general one dimensional random systems. I: Jacobi matrices

DOI10.1007/BF01229383zbMath0604.60062OpenAlexW2092804045MaRDI QIDQ1083124

Barry Simon

Publication date: 1985

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01229383

zbMATH Keywords

Lyapunov exponentrandom discrete Schrödinger operators

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Stochastic mechanics (including stochastic electrodynamics) (81P20)

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Cites Work

• Kotani theory for one dimensional stochastic Jacobi matrices
• One-dimensional Schrödinger operators with random or deterministic potentials: New spectral types
• Constructive proof of localization in the Anderson tight binding model
• Anderson localization for multi-dimensional systems at large disorder or large energy
• Localization in general one-dimensional random systems. II: Continuum Schrödinger operators
• Ergodic theory of differentiable dynamical systems
• Sur le spectre des opérateurs aux différences finies aléatoires
• Almost periodic Schrödinger operators. III: The absolutely continuous spectrum in one dimension
• On a Problem of Weyl in the Theory of Singular Sturm-Liouville Equations
• Singular continuous spectrum under rank one perturbations and localization for random hamiltonians
• On the perturbation of spectra
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