Concentration of the Spectral Measure for Large Random Matrices with Stable Entries

TL;DR

This paper establishes concentration inequalities for spectral measures of large random matrices with stable and infinitely divisible entries, providing insights into eigenvalue and singular value behaviors.

Contribution

It introduces new concentration inequalities for spectral measures of large matrices with stable entries, extending understanding of their spectral properties.

Findings

Concentration inequalities for empirical spectral measures.

Results on the largest eigenvalue and singular value.

Applicability to matrices with stable, infinitely divisible entries.

Abstract

We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these random matrices, such as the largest eigenvalue or the largest singular value.