Generalized eigenvalue-counting estimates for the Anderson model

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.

Minor revision

References in corpus (7)

• Finite-Volume Fractional-Moment Criteria for Anderson Localization
• New characterizations of the region of complete localization for random Schrödinger operators
• Correlations Estimates in the Lattice Anderson Model
• Simplicity of eigenvalues in the Anderson model
• On Mott's formula for the ac-conductivity in the Anderson model
• Poisson statistics of eigenvalues in the hierarchical Anderson model
• The repulsion between localization centers in the Anderson model

Cited by in corpus (19)

• The scaling limit of the critical one-dimensional random Schrodinger operator
• Resonances for large one-dimensional "ergodic" systems
• An eigensystem approach to Anderson localization
• Minami's estimate: beyond rank one perturbation and monotonicity
• On the Wegner orbital model
• Eigenvalue statistics for random Schrodinger operators with non rank one perturbations
• Decorrelation estimates for the eigenlevels of the discrete Anderson model in the localized regime
• Ground state energy of trimmed discrete Schrödinger operators and localization for trimmed Anderson models
• Matrix regularizing effects of Gaussian perturbations
• Conductivity and the current-current correlation measure
• Renormalization Group Analysis of the Hierarchical Anderson Model
• Level Spacing for Non-Monotone Anderson Models
• Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials
• Decorrelation estimates for some continuous and discrete random schrödinger operators in dimension one and applications to spectral statistics
• On the Sum of the Non-Negative Lyapunov Exponents for Some Cocycles Related to the Anderson Model
• Eigensystem multiscale analysis for the Anderson model via the Wegner estimate
• Eigenfunction Statistics for Anderson Model with Hölder continuous single site Potential
• A bound on the averaged spectral shift function and a lower bound on the density of states for random Schrödinger operators on ${\mathbb{R}}^d$
• Eigenvectors of the square grid plus GUE