Random permutations with cycle weights

Details Random permutations with cycle weights Random permutations with cycle weights

2009-08-17

arxiv.org/abs/0908.2217v3

Annals of Applied Probability 2011, Vol. 21, No. 1, 312-331

Mathematics

Probability

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

Scientific paper

10.1214/10-AAP697

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 $n$.

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