Abstract:
Probability measures on the space of Hermitian matrices which are ergodic for the conjugation action of an infinite-dimensional unitary group are considered. It is established that the eigenvalues of random matrices distributed with respect to these measures satisfy the law of large numbers. The relationship between such models of random matrices and objects in free probability, freely infinitely divisible measures, is also established.
Keywords:unitarily invariant ergodic matrix, infinitely divisible measure, free probability, Hermitian matrix, empiric distribution of eigenvalues, free convolution, free cumulant.
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