Riemann-Hilbert approach to multi-time processes: The Airy and the Pearcey cases

被引：17

作者：

Bertola, M. ^{[1
]}

Cafasso, M.

机构：

[1] Univ Montreal, Ctr Rech Math, Succ Ctr Ville, Montreal, PQ H3C 3J7, Canada

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2012年 / 241卷 / 23-24期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Random point processes; Riemann-Hilbert problems; Integrable kernels; GAUSSIAN RANDOM MATRICES; LARGE-N LIMIT; EXTERNAL SOURCE; DYSON;

D O I：

10.1016/j.physd.2012.01.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that matrix Fredholm determinants related to multi-time processes can be expressed in terms of determinants of integrable kernels a la Its-Izergin-Korepin-Slaynov (IIKS) and hence related to suitable Riemann-Hilbert problems, thus extending the known results for the single-time case. We focus on the Airy and Pearcey processes. As an example of applications we re-deduce a third order POE, found by Adler and van Moerbeke, for the two-time Airy process. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：2237 / 2245

页数：9

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