Central Limit Theorem for Multiplicative Class Functions on the Symmetric Group

Dirk Zeindler ()
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Dirk Zeindler: University of York

Journal of Theoretical Probability, 2013, vol. 26, issue 4, 968-996

Abstract: 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.

Keywords: Symmetric group; Ewens measure; Characteristic polynomial; Multiplicative class function; Wasserstein distance; 60B20; 60F05 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10959-011-0382-3

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