Concentration of distances in Wigner matrices

TL;DR

This paper extends the known concentration of distances in iid matrices to Wigner matrices, providing exponential bounds for the lower tail, thus broadening understanding of spectral properties in random matrix theory.

Contribution

The paper introduces new concentration results for distances in Wigner matrices, including exponential tail bounds, which were previously established mainly for iid matrices.

Findings

Distances in Wigner matrices are highly concentrated around their mean.

Exponential bounds for the lower tail of these distances are derived.

The results generalize known concentration phenomena from iid matrices to Wigner matrices.

Abstract

It is well-known that distances in random iid matrices are highly concentrated around their mean. In this note we extend this concentration phenomenon to Wigner matrices. Exponential bounds for the lower tail are also included.