On statistics of permutations chosen from the Ewens distribution (Q6486654)

In this paper the asymptotic distributions of sequences of integer-valued additive functions defined on the symmetric group endowed with the Ewens probability measures as the order of group increases are explored. By using of the method of factorial moments, the necessary and sufficient conditions for the weak convergence of distribution to discrete laws are obtained. The number-of cycles function is analysed in more detail. The results of this paper can be applied to statistics defined on random permutation matrices.