Asymptotic expansion for multiplicative statistics in a Hermitian matrix model connected to the lower tail of the KPZ equation

TL;DR

This paper extends the analysis of multiplicative statistics in unitary matrix models with a growing parameter, connecting it to the lower tail behavior of the KPZ equation, and provides asymptotic expansions for these statistics.

Contribution

It introduces an asymptotic expansion for multiplicative statistics in a deformed Hermitian matrix model with a growing parameter, linking it to KPZ lower tail analysis.

Findings

Extended previous results to a growing parameter regime

Established connection between matrix statistics and KPZ lower tail

Derived asymptotic expansions for the deformed matrix model

Abstract

We explore the multiplicative statistics for a unitary random matrix ensemble with a parameter-dependent deformation inserted in the probability measure. Such deformations had been studied for a bounded or decaying parameter. In this work, we extend the previous results for a growing parameter under a controlled rate, and show that the underlying statistics relate to the lower tail study for the KPZ equation.