Spectral statistics for random Schrödinger operators in the localized regime

DOI10.4171/JEMS/481zbMath1330.81092arXiv1011.1832OpenAlexW2963669659MaRDI QIDQ479517

Frédéric Klopp, François Germinet

Publication date: 5 December 2014

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.1832

zbMATH Keywords

random Schrödinger operatorslevel spacing distributioneigenvalue statistics

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Random operators and equations (aspects of stochastic analysis) (60H25) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) PDEs with randomness, stochastic partial differential equations (35R60) Random linear operators (47B80)

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Cites Work

• Moment analysis for localization in random Schrödinger operators
• Smoothness of the density of states in the Anderson model at high disorder
• Localization at large disorder and at extreme energies: an elementary derivation
• Generalized eigenvalue-counting estimates for the Anderson model
• Correlation estimates in the Anderson model
• LOCALIZATION AT WEAK DISORDER: SOME ELEMENTARY BOUNDS
• Finite-volume fractional-moment criteria for Anderson localization

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