Asymptotics for a determinant with a confluent hypergeometric kernel

TL;DR

This paper derives large gap asymptotics for Fredholm determinants involving confluent hypergeometric and Bessel kernels, relevant in random matrix theory, providing insights into their asymptotic behavior.

Contribution

It introduces new asymptotic formulas for determinants with confluent hypergeometric and Bessel kernels, expanding understanding of their large gap behavior.

Findings

Large gap asymptotics for confluent hypergeometric kernel determinants

Asymptotic results for Bessel kernel determinants in random matrix theory

Enhanced understanding of kernel behavior in asymptotic regimes

Abstract

We obtain "large gap" asymptotics for a Fredholm determinant with a confluent hypergeometric kernel. We also obtain asymptotics for determinants with two types of Bessel kernels which appeared in random matrix theory.