Smoothness of integrated density of states of the Anderson model on Bethe lattice in high disorder

TL;DR

This paper proves that in the high disorder regime, the integrated density of states for the Anderson model on a Bethe lattice shares the same level of smoothness as the single site distribution.

Contribution

It establishes the smoothness of the IDS in the Anderson model on Bethe lattices under high disorder, linking it directly to the SSD.

Findings

IDS is as smooth as the SSD in high disorder

Provides rigorous proof for smoothness property

Enhances understanding of spectral properties in disordered systems

Abstract

In this work we consider the Anderson model on Bethe lattice and prove that the integrated density of states (IDS) is as smooth as the single site distribution (SSD), in high disorder