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Central Limit Theorem for Multiplicative Class Functions on the Symmetric Group

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  • Dirk Zeindler

    (University of York)

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.

Suggested Citation

  • Dirk Zeindler, 2013. "Central Limit Theorem for Multiplicative Class Functions on the Symmetric Group," Journal of Theoretical Probability, Springer, vol. 26(4), pages 968-996, December.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:4:d:10.1007_s10959-011-0382-3
    DOI: 10.1007/s10959-011-0382-3
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    References listed on IDEAS

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    1. Hambly, B. M. & Keevash, P. & O'Connell, N. & Stark, D., 2000. "The characteristic polynomial of a random permutation matrix," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 335-346, December.
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    Cited by:

    1. Valentin Bahier, 2019. "On the Number of Eigenvalues of Modified Permutation Matrices in Mesoscopic Intervals," Journal of Theoretical Probability, Springer, vol. 32(2), pages 974-1022, June.

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