An estimate for the average spectral measure of random band matrices

TL;DR

This paper investigates the spectral properties of random band matrices, establishing regularity and asymptotic behavior of their average spectral measure at specific scales related to the band width.

Contribution

It provides new results on the regularity and asymptotic estimates of the average spectral measure for a class of random band matrices.

Findings

Spectral measure is regular at scales   W^{-0.99}

Asymptotic behavior of the spectral measure is characterized at these scales

Results apply to a class of random band matrices with band width W

Abstract

For a class of random band matrices of band width $W$, we prove regularity of the average spectral measure at scales $\epsilon \geq W^{-0.99}$, and find its asymptotics at these scales.