The Annals of Applied Probability

Random permutations with cycle weights

Volker Betz, Daniel Ueltschi, and Yvan Velenik

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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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Ann. Appl. Probab. Volume 21, Number 1 (2011), 312-331.

First available in Project Euclid: 17 December 2010

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Random permutations cycle weights cycle lengths Ewens distribution


Betz, Volker; Ueltschi, Daniel; Velenik, Yvan. Random permutations with cycle weights. Ann. Appl. Probab. 21 (2011), no. 1, 312--331. doi:10.1214/10-AAP697.

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