Spectral Statistics for an Anderson Model with sporadic potentials

TL;DR

This paper investigates the spectral properties of an Anderson model with many sites having zero interaction, demonstrating that Poisson statistics applies in the localized regime through the proof of the Minami estimate.

Contribution

It introduces a spectral analysis of an Anderson model with sporadic potentials and proves Poisson spectral statistics in the localized phase.

Findings

Poisson statistics holds for the model's localized energies

Proof of the Minami estimate for the model

Spectral localization established in the studied regime

Abstract

In this paper we consider an Anderson model with a large number of sites with zero interaction. For such models we study the spectral statistics in the region of complete localization. We show that Poisson statistics holds for such energies, by proving the Minami estimate.