The multiplicative constant for the Meijer-$G$ kernel determinant

TL;DR

This paper calculates the precise multiplicative constant in the large gap asymptotics of the Meijer-G point process, which is relevant in advanced random matrix theory and generalizes known processes like the Bessel point process.

Contribution

It provides the first explicit computation of the multiplicative constant for the Meijer-G kernel determinant in large gap asymptotics.

Findings

Explicit multiplicative constant derived for the Meijer-G kernel

Results applicable to Cauchy--Laguerre multi-matrix models

Enhances understanding of large gap asymptotics in random matrix theory

Abstract

We compute the multiplicative constant in the large gap asymptotics of the Meijer-G point process. This point process generalizes the Bessel point process and appears at the hard edge of Cauchy--Laguerre multi-matrix models and of certain product random matrix ensembles.