Sharp Bounds for the Integrated Density of States of a Strongly Disordered 1D Anderson-Bernoulli Model

TL;DR

This paper establishes uniform upper and lower bounds for the integrated density of states in a strongly disordered 1D Anderson-Bernoulli model, revealing explicit IDS values at specific energies independent of disorder strength.

Contribution

It provides the first explicit bounds for the IDS in a strongly disordered 1D Anderson-Bernoulli model, applicable across the entire spectrum.

Findings

Bounds are uniform over the spectrum.

Existence of energies with explicit IDS values independent of disorder.

Spectral bands are separated by strong disorder.

Abstract

In this article we give upper and lower bounds for the integrated density of states (IDS) of the 1D discrete Anderson-Bernoulli model when the disorder is strong enough to separate the two spectral bands. These bounds are uniform on the disorder and hold over the whole spectrum. They show the existence of a sequence of energies in which the value of the IDS can be given explicitly and does not depend on the disorder parameter.