Airy-kernel determinant on two large intervals

TL;DR

This paper calculates the probability of two specific large gaps in the eigenvalue distribution of the Gaussian Unitary Ensemble, providing precise asymptotics including the multiplicative constant.

Contribution

It derives the asymptotic probability of two large gaps in GUE eigenvalues with explicit constants, extending understanding of edge scaling limits.

Findings

Explicit asymptotics for two-gap probabilities in GUE

Inclusion of multiplicative constants in asymptotic formulas

Enhanced understanding of eigenvalue gap distributions

Abstract

We find the probability of two gaps of the form $(sc,sb)\cup (sa,+\infty)$, $c<b<a<0$, for large $s>0$, in the edge scaling limit of the Gaussian Unitary Ensemble of random matrices, including the multiplicative constant in the asymptotics.