Edgeworth expansion of the largest eigenvalue distribution function of Gaussian orthogonal ensemble

被引：4

作者：

Choup, Leonard N. ^{[1
]}

机构：

[1] Univ Alabama, Dept Math Sci, Huntsville, AL 35899 USA

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2009年 / 50卷 / 01期

关键词：

eigenvalues and eigenfunctions; functional analysis; Gaussian processes; matrix algebra; probability; random processes; SPACING DISTRIBUTIONS;

D O I：

10.1063/1.3046561

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper we focus on the large n probability distribution function of the largest eigenvalue in the Gaussian orthogonal ensemble of nxn matrices (GOE(n)). We prove an Edgeworth-type theorem for the largest eigenvalue probability distribution function of GOE(n). The correction terms to the limiting probability distribution are expressed in terms of the same Painleve II functions appearing in the Tracy-Widom distribution. We conclude with a brief discussion of the GSE(n) case.

引用

页数：22

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