Symmetry 2011, 3(3), 600-610; doi:10.3390/sym3030600
Article

High-Dimensional Random Matrices from the Classical Matrix Groups, and Generalized Hypergeometric Functions of Matrix Argument

Department of Statistics, Pennsylvania State University, University Park, PA 16802-2111, USA
Received: 27 May 2011; in revised form: 16 August 2011 / Accepted: 23 August 2011 / Published: 26 August 2011
(This article belongs to the Special Issue Symmetry in Probability and Inference)
PDF Full-text Download PDF Full-Text [227 KB, uploaded 26 August 2011 12:47 CEST]
Abstract: Results from the theory of the generalized hypergeometric functions of matrix argument, and the related zonal polynomials, are used to develop a new approach to study the asymptotic distributions of linear functions of uniformly distributed random matrices from the classical compact matrix groups. In particular, we provide a new approach for proving the following result of D’Aristotile, Diaconis, and Newman: Let the random matrix Hn be uniformly distributed according to Haar measure on the group of n × n orthogonal matrices, and let An be a non-random n × n real matrix such that tr (A'nAn) = 1. Then, as n→∞, √n tr AnHn converges in distribution to the standard normal distribution.
Keywords: Generalized hypergeometric function of matrix argument; normal approximation; orthogonal matrix; random matrix; Stiefel manifold; symplectic matrix; unitary matrix; zonal polynomial

Article Statistics

Load and display the download statistics.

Citations to this Article

Cite This Article

MDPI and ACS Style

Richards, D.S.P. High-Dimensional Random Matrices from the Classical Matrix Groups, and Generalized Hypergeometric Functions of Matrix Argument. Symmetry 2011, 3, 600-610.

AMA Style

Richards DSP. High-Dimensional Random Matrices from the Classical Matrix Groups, and Generalized Hypergeometric Functions of Matrix Argument. Symmetry. 2011; 3(3):600-610.

Chicago/Turabian Style

Richards, Donald St. P. 2011. "High-Dimensional Random Matrices from the Classical Matrix Groups, and Generalized Hypergeometric Functions of Matrix Argument." Symmetry 3, no. 3: 600-610.

Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert