Large gaps of CUE and GUE

TL;DR

This paper investigates the largest gaps in classical random matrices from CUE and GUE, demonstrating that their rescaled limiting densities follow Gumbel distributions, revealing new statistical properties of these matrices.

Contribution

It establishes the limiting distribution of the largest gaps in CUE and GUE matrices as Gumbel, providing new insights into their spectral gap behavior.

Findings

Largest gaps follow Gumbel distribution after rescaling

Limiting densities of gaps are characterized explicitly

Provides new understanding of spectral gap statistics in random matrices

Abstract

In this article, we study the largest gaps of the classical random matrices of CUE and GUE, and show that after rescaling, the limiting densities are given by the Gumbel distributions.