# Localization and Eigenvalue Statistics for the Lattice Anderson model with Discrete Disorder

## TL;DR

This paper proves localization and bounds on energy level spacing for the lattice Anderson model with a large discrete disorder distribution, advancing understanding of spectral properties in disordered quantum systems.

## Contribution

It establishes localization and probabilistic bounds for the Anderson model with large discrete disorder, extending previous results to models with many potential values.

## Key findings

- Proves localization in the Anderson model with discrete disorder.
- Provides probabilistic bounds on minimum energy level spacing.
- Applicable to models with large discrete potential distributions.

## Abstract

We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.