On the number of cycles in a random permutation

Kenneth Maples (Universität Zürich)
Ashkan Nikeghbali (Universität Zürich)
Dirk Zeindler (Universität Bielefeld)

Abstract


We show that the number of cycles in a random permutation chosen according to generalized Ewens measure is normally distributed and compute asymptotic estimates for the mean and variance.

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Pages: 1-13

Publication Date: May 27, 2012

DOI: 10.1214/ECP.v17-1934

References

  • Arratia, Richard; Barbour, Andrew; Tavaré, Simon. Logarithmic combinatorial structures: a probabilistic approach. EMS Monographs in Mathematics. European Mathematical Society (EMS), Zürich, 2003. xii+363 pp. ISBN: 3-03719-000-0 MR2032426
  • Betz, Volker; Ueltschi, Daniel. Spatial random permutations and Poisson-Dirichlet law of cycle lengths. Electron. J. Probab. 16 (2011), no. 41, 1173--1192. MR2820074
  • Betz, Volker; Ueltschi, Daniel. Spatial random permutations and infinite cycles. Comm. Math. Phys. 285 (2009), no. 2, 469--501. MR2461985
  • Betz, Volker; Ueltschi, Daniel; Velenik, Yvan. Random permutations with cycle weights. Ann. Appl. Probab. 21 (2011), no. 1, 312--331. MR2759204
  • Ercolani, Nicholas; Ueltschi, Daniel. Cycle structure of random permutations with cycle weights. Preprint 2011
  • Flajolet, Philippe; Sedgewick, Robert. Analytic combinatorics. Cambridge University Press, Cambridge, 2009. xiv+810 pp. ISBN: 978-0-521-89806-5 MR2483235
  • Nikeghbali, Ashkan; Zeindler, Dirk. The generalized weighted probability measure on the symmetric group and the asymptotic behaviour of the cycles, To appear in Annales de L'Institut Poincaré, 2011.
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