## Eigenvalues of random wreath products.(English)Zbl 1013.15006

The author considers the limiting distribution of eigenvalues of random elements of the $$n$$-fold wreath product of a finite transitive permutation group. It is proved that there is weak convergence in probability to the standard Lebesgue measure on the unit circle. This is a corollary of a stronger result that the limiting probability that expectation of trigonometic polynomial is not its expectation under Lebesgue measure is zero. The result is extended to a class of infinite Fourier series.

### MSC:

 15B52 Random matrices (algebraic aspects) 42A20 Convergence and absolute convergence of Fourier and trigonometric series 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 15A18 Eigenvalues, singular values, and eigenvectors 05C05 Trees 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
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