Random permutations with cycle weights

Volker Betz; Daniel Ueltschi; Yvan Velenik

doi:10.1214/10-AAP697

Random permutations with cycle weights

Probability 2011-01-06 v3 Combinatorics

Authors: Volker Betz , Daniel Ueltschi , Yvan Velenik

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Abstract

We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number $n$ of elements, or a fraction of $n$ or a logarithmic power of $n$ .

Keywords

permutations dynamical systems probability distribution

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@article{arxiv.0908.2217,
  title  = {Random permutations with cycle weights},
  author = {Volker Betz and Daniel Ueltschi and Yvan Velenik},
  journal= {arXiv preprint arXiv:0908.2217},
  year   = {2011}
}

Comments

Published in at http://dx.doi.org/10.1214/10-AAP697 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Random permutations with cycle weights

Abstract

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