On the eigenvalues of random matrices. (English) Zbl 0807.15015

Diaconis, Persi; Shahshahani, Mehrdad

J. Appl. Probab. 31A, Spec. Vol., 49-62 (1994).

The paper deals with a continuous generalization to the classical compact groups: orthogonal, unitary and symplectic. Throughout, random mean uniformly (Haar) distributed. The main results show that the trace of a randomly chosen matrix has an approximate Gaussian distribution.
Gaussian approximations for powers of random matrices are also derived and to results for the distribution of their eigenvalues.

Reviewer: Seshadri Sridhar (Madras)

MSC:

15B52	Random matrices (algebraic aspects)
15A42	Inequalities involving eigenvalues and eigenvectors
60F05	Central limit and other weak theorems

Keywords:

random matrices; orthogonal group; unitary group; symplectic group; eigenvalue distribution; compact groups; Gaussian distribution