ON THE VARIANCE OF THE INDEX FOR THE GAUSSIAN UNITARY ENSEMBLE

被引：7

作者：

Witte, N. S. ^{[1
]}

Forrester, P. J. ^{[1
]}

机构：

[1] Univ Melbourne, Dept Math & Stat, Melbourne, Vic 3010, Australia

来源：

RANDOM MATRICES-THEORY AND APPLICATIONS | 2012年 / 1卷 / 04期

基金：

澳大利亚研究理事会;

关键词：

Random matrices; large deviations; Painleve equations;

D O I：

10.1142/S2010326312500104

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We derive simple linear, inhomogeneous recurrences for the variance of the index by utilizing the fact that the generating function for the distribution of the number of positive eigenvalues of a Gaussian unitary ensemble is a tau-function of the fourth Painleve equation. From this we deduce a simple summation formula, several integral representations and finally an exact hypergeometric function evaluation for the variance.

引用

页数：25

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