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Central limit theorem for multiplicative class function on the symmetric group

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>12/2013
<mark>Journal</mark>Journal of Theoretical Probability
Issue number4
Volume26
Number of pages29
Pages (from-to)968-996
Publication StatusPublished
<mark>Original language</mark>English

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.