Lifshitz tails estimate for the density of states of the Anderson model

TL;DR

This paper establishes an upper bound on the density of states for the Anderson model at low energies, demonstrating Lifshitz tail behavior similar to that of the integrated density of states.

Contribution

It provides a new upper bound for the density of states at the spectrum's bottom, aligning it with Lifshitz tail estimates for the integrated density of states.

Findings

Density of states exhibits Lifshitz tail behavior.

Upper bound matches Lifshitz tail estimates.

Results apply to the differentiated density of states.

Abstract

We prove an upper bound for the (differentiated) density of states of the Anderson model at the bottom of the spectrum. The density of states is shown to exhibit the same Lifshitz tails upper bound as the integrated density of states.