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.
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页数：25
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