The Annals of Applied Probability

Random permutations with cycle weights

Volker Betz, Daniel Ueltschi, and Yvan Velenik

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 17 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1292598036

Digital Object Identifier
doi:10.1214/10-AAP697

Mathematical Reviews number (MathSciNet)
MR2759204

Zentralblatt MATH identifier
1226.82003

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

Keywords
Random permutations cycle weights cycle lengths Ewens distribution

Citation

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. https://projecteuclid.org/euclid.aoap/1292598036


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