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.
All Science Journal Classification (ASJC) codes
- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- General Mathematics
- Physics and Astronomy (miscellaneous)