Generalized Eigenvalue-Counting Estimates for the Anderson Model

2008/04/30 by Jean-Michel Combes, François Germinet, Abel Klein · 2 citations
Mathematics · Physics and Astronomy · #Anderson impurity model #Anderson localization #Distribution (mathematics) #Eigenvalues and eigenvectors #Multiplicity (mathematics) #Probability distribution #Probability measure #Probability theory #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics #math-ph #math.MP #msc:47B80 #msc:60H25 #msc:82B44

paper · pdf · doi:10.1007/s10955-009-9731-3

Minor revision

arxiv created 2009/03/19 · openalex publication_date 2009/04/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We generalize Minami’s estimate for the Anderson model and its extensions to n eigenvalues, allowing for n arbitrary intervals and arbitrary single-site probability measures with no atoms. As an application, we derive new results about the multiplicity of eigenvalues and Mott’s formula for the ac-conductivity when the single site probability distribution is Hölder continuous.

Citations

• Anderson localization for Bernoulli and other singular potentials
• Bootstrap Multiscale Analysis and Localization¶in Random Media
• Correlation Estimates in the Anderson Model
• Singular continuous spectrum under rank one perturbations and localization for random hamiltonians

Cited by

• Decorrelation Estimates for Random Discrete Schrödinger Operators in Dimension One and Applications to Spectral Statistics
• Decorrelation Estimates for the Eigenlevels of the Discrete Anderson Model in the Localized Regime

Related

• On Eigenvalue spacings for the 1-D Anderson model with singular site distribution
• On the distribution of linear combinations of eigenvalues of the Anderson model
• Enhanced Wegner and Minami estimates and eigenvalue statistics of random Anderson models at spectral edges
• Spectral Statistics for an Anderson Model with sporadic potentials
• Eigenvalue counting inequalities, with applications to Schrodinger operators