Central limit theorem for multiplicative class functions on the symmetric group

Details Central limit theorem for multiplicative class functions on the symmetric group Central limit theorem for multiplicative class functions on the symmetric group

2010-10-26

arxiv.org/abs/1010.5361v3

Mathematics

Probability

23 pages; the mathematics is the same as in the previous version, but there are several improvments in the presentation, inclu

Scientific paper

10.1007/s10959-011-0382-3

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 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.

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