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The characteristic polynomial of a random permutation matrix at different points

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  • Dang, K.
  • Zeindler, D.

Abstract

We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show that the behavior at different points is independent in the limit and are asymptotically normal. Our methods enable us to study also the wreath product of permutation matrices and diagonal matrices with i.i.d. entries and more general class functions on the symmetric group with a multiplicative structure.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:1:p:411-439
    DOI: 10.1016/j.spa.2013.08.003
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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. Bahier, Valentin, 2019. "Characteristic polynomials of modified permutation matrices at microscopic scale," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4335-4365.
    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.

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