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The characteristic polynomial of a random permutation matrix

Author

Listed:
  • Hambly, B. M.
  • Keevash, P.
  • O'Connell, N.
  • Stark, D.

Abstract

We establish a central limit theorem for the logarithm of the characteristic polynomial of a random permutation matrix. We relate this result to a central limit theorem of Wieand for the counting function for the eigenvalues lying in some interval on the unit circle.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:90:y:2000:i:2:p:335-346
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    Citations

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    Cited by:

    1. Dang, K. & Zeindler, D., 2014. "The characteristic polynomial of a random permutation matrix at different points," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 411-439.
    2. 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.
    3. Kelly Wieand, 2003. "Permutation Matrices, Wreath Products, and the Distribution of Eigenvalues," Journal of Theoretical Probability, Springer, vol. 16(3), pages 599-623, July.
    4. 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.
    5. Chafaï, Djalil, 2010. "The Dirichlet Markov Ensemble," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 555-567, March.
    6. Bahier, Valentin, 2019. "Characteristic polynomials of modified permutation matrices at microscopic scale," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4335-4365.

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