Central limit theorem for multiplicative class function on the symmetric group

Zeindler, Dirk (2013) Central limit theorem for multiplicative class function on the symmetric group. Journal of Theoretical Probability, 26 (4). pp. 968-996. ISSN 1572-9230

Abstract

Hambly, Keevash, O’Connell, and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We prove here a central limit theorem for multiplicative class functions on the symmetric group with respect to the Ewens measure and compute the covariance of the real and the imaginary part in the limit. We also estimate the rate of convergence with the Wasserstein distance.