Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles

被引：46

作者：

Jiang, Tiefeng ^{[1
]}

机构：

[1] Univ Minnesota, Sch Stat, Minneapolis, MN 55455 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2009年 / 144卷 / 1-2期

关键词：

Haar measure; Eigenvalue; Random matrix; Largest eigenvalue; Empirical distribution; Limiting distribution; SMALLEST EIGENVALUE; SPECTRAL-ANALYSIS; ROOTS; THEOREMS; ENTRIES; MODELS; BOUNDS;

D O I：

10.1007/s00440-008-0146-x

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We develop a tool to approximate the entries of a large dimensional complex Jacobi ensemble with independent complex Gaussian random variables. Based on this and the author's earlier work in this direction, we obtain the Tracy-Widom law of the largest singular values of the Jacobi emsemble. Moreover, the circular law, the Marchenko-Pastur law, the central limit theorem, and the laws of large numbers for the spectral norms are also obtained.

引用

页码：221 / 246

页数：26

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