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Central Limit Theorem for Multiplicative Class Functions on the Symmetric Group

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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.

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  1. Department of Mathematics, University of York, York, YO10 5DD, UK

    Dirk Zeindler

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  1. Dirk Zeindler
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Correspondence to Dirk Zeindler.

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Zeindler, D. Central Limit Theorem for Multiplicative Class Functions on the Symmetric Group. J Theor Probab 26, 968–996 (2013). https://doi.org/10.1007/s10959-011-0382-3

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  • DOI: https://doi.org/10.1007/s10959-011-0382-3

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