Central limit theorem in the symmetric group

Abstract

In this work we investigate a rate of convergence of sums of random variables defined on a symetric group S_n, when the probability measure on S_n is defined by the Ewens sampling formula with parameter θ. Using the results obtained by E. Manstavičius in paper [1] for the case when θ = 1, we obtain their analogs, when θ > 1, thus estimating the closenes of distribution of h(σ) to normal distribution.