Asymptotics of tracy-widom distributions and the total integral of a painleve II function

被引：110

作者：

Baik, Jinho ^{[1
]}

Buckingham, Robert ^{[1
]}

DiFranco, Jeffery ^{[2
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Seattle Univ, Dept Math, Seattle, WA 98122 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2008年 / 280卷 / 02期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1007/s00220-008-0433-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The Tracy-Widom distribution functions involve integrals of a Painleve II function starting from positive infinity. In this paper, we express the Tracy-Widom distribution functions in terms of integrals starting from minus infinity. There are two consequences of these new representations. The first is the evaluation of the total integral of the Hastings-McLeod solution of the Painleve II equation. The second is the evaluation of the constant term of the asymptotic expansions of the Tracy-Widom distribution functions as the distribution parameter approaches minus infinity. For the GUE Tracy-Widom distribution function, this gives an alternative proof of the recent work of Deift, Its, and Krasovsky. The constant terms for the GOE and GSE Tracy-Widom distribution functions are new.

引用

页码：463 / 497

页数：35

共 28 条

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