Distribution of the smallest eigenvalue in complex and real correlated Wishart ensembles

被引：6

作者：

Wirtz, Tim ^{[1
]}

Guhr, Thomas ^{[1
]}

机构：

[1] Univ Duisburg Essen, Fak Phys, Duisburg, Germany

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2014年 / 47卷 / 07期

关键词：

random matrix theory; supersymmetry; multivariate statistics; correlated Wishart matrices; universality; RANDOM-MATRIX THEORY; QCD DIRAC OPERATOR; CHIRAL-SYMMETRY; SPECTRUM; SYSTEMS;

D O I：

10.1088/1751-8113/47/7/075004

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

VVFor the correlated Gaussian-Wishart ensemble we compute the distribution of the smallest eigenvalue and a related gap probability. We obtain exact results for the complex (beta = 2) and for the real case (beta = 1). For a particular set of empirical correlation matrices we find universality in the spectral density, for both real and complex ensembles and all kinds of rectangularity. We calculate the asymptotic and universal results for the gap probability and the distribution of the smallest eigenvalue. We use the supersymmetry method, in particular the generalized Hubbard-Stratonovich transformation and superbosonization.

引用

页数：28

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