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

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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

All Science Journal Classification (ASJC) codes

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

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