论皮尔斯过程的生成函数

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2021-07-05 DOI:10.1214/22-aap1890

C. Charlier, P. Moreillon

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引用次数: 5

摘要

皮尔斯过程是随机矩阵理论中的一个普适点过程。本文研究了任意数$m$区间上的peararcey过程的生成函数。我们用哈密顿函数的形式推导了它的一个积分表示，这个哈密顿函数与一个$ 600 + $ 2耦合非线性方程的系统有关。我们也得到了生成函数的渐近性，当区间的大小变大，直到并包括常数项。本文推广了Dai, Xu和Zhang最近的一些结果，这些结果对应于$m=1$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the generating function of the Pearcey process

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 $m=1$.

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来源期刊

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.