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 (3)

• Correlations Estimates in the Lattice Anderson Model
• Poisson statistics of eigenvalues in the hierarchical Anderson model
• The repulsion between localization centers in the Anderson model