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

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.

MSC:

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