The Integrated Density of States of the 1D Discrete Anderson-Bernoulli Model at Rational Energies

TL;DR

This paper identifies a dense set of energies in the 1D Anderson-Bernoulli model where the integrated density of states can be explicitly calculated, independent of disorder strength above a certain threshold.

Contribution

It provides explicit formulas for the integrated density of states at rational energies, revealing disorder independence above a threshold.

Findings

Existence of a countable dense set of energies with explicit IDS formulas

IDS independence from disorder parameter above a threshold

Explicit characterization of IDS at rational energies

Abstract

We show there is a countable dense set of energies at which the integrated density of states of the 1D discrete Anderson-Bernoulli model can be given explicitly and does not depend on the disorder parameter, provided the latter is above an energy-dependent threshold.