High-dimensional random matrices from the classical matrix groups, and generalized hypergeometric functions of matrix argument

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7 Citations (Scopus)

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 H n be uniformly distributed according to Haar measure on the group of n × n orthogonal matrices, and let A n be a non-random n × n real matrix such that tr (A′ nA n) = 1. Then, as n → ∞, √n tr A nH n converges in distribution to the standard normal distribution.

Original languageEnglish (US)
Pages (from-to)600-610
Number of pages11
JournalSymmetry
Volume3
Issue number3
DOIs
StatePublished - Sep 1 2011

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Generalized Hypergeometric Function
hypergeometric functions
Matrix Groups
Classical Groups
Random Matrices
High-dimensional
Zonal Polynomials
Standard Normal distribution
Orthogonal matrix
Haar Measure
Compact Group
matrices
Linear Function
Asymptotic distribution
Converge
normal density functions
polynomials
Normal distribution
Polynomials

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

Cite this

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