Eigenvalues of random wreath products
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.
scientific article; zbMATH DE number 1868588