The Entries of Haar-Invariant Matrices from the Classical Compact Groups

被引：19

作者：

Jiang, Tiefeng ^{[1
]}

机构：

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

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2010年 / 23卷 / 04期

关键词：

Random matrix; Haar measure; Classical compact group; Probability inequality; Independence; Gaussian distribution; THEOREMS;

D O I：

10.1007/s10959-009-0241-7

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：

Let Gamma(n) = (gamma(ij))(nxn) be a random matrix with the Haar probability measure on the orthogonal group O(n), the unitary group U(n), or the symplectic group Sp(n). Given 1 <= m < n, a probability inequality for a distance between (gamma(ij))(nxm) and some mn independent F-valued normal random variables is obtained, where F = R, C, or H (the set of real quaternions). The result is universal for the three cases. In particular, the inequality for Sp(n) is new.

引用

页码：1227 / 1243

页数：17

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