Asymptotics of the Airy-kernel determinant

TL;DR

This paper employs Riemann-Hilbert techniques to precisely determine the constant in the asymptotic expansion of the Airy-kernel determinant, a key quantity in random matrix theory.

Contribution

It provides a rigorous computation of the constant term in the asymptotics of the Airy-kernel determinant, advancing understanding of edge statistics in random matrices.

Findings

Explicit value of the constant in the asymptotic expansion

Enhanced understanding of edge behavior in random matrix ensembles

Application of Riemann-Hilbert methods to kernel determinants

Abstract

The authors use Riemann-Hilbert methods to compute the constant that arises in the asymptotic behavior of the Airy-kernel determinant of random matrix theory.