On the generating function of the Pearcey process

TL;DR

This paper derives an integral representation and asymptotic analysis for the generating function of the Pearcey process across multiple intervals, extending previous results for a single interval.

Contribution

It generalizes existing results by providing a comprehensive integral and asymptotic framework for the Pearcey process on any number of intervals.

Findings

Integral representation in terms of a Hamiltonian system.

Asymptotic formulas for large interval sizes.

Extension of previous single-interval results to multiple intervals.

Abstract

The Pearcey process is a universal point process in random matrix theory. In this paper, we study the generating function of the Pearcey process on any number $m$ of intervals. We derive an integral representation for it in terms of a Hamiltonian that is related to a system of $6m+2$ coupled nonlinear equations. We also obtain asymptotics for the generating function as the size of the intervals get large, up to and including the constant term. This work generalizes some recent results of Dai, Xu and Zhang, which correspond to $m=1$.