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Cycle structure of random permutations with cycle weights

By Nicholas M. Ercolani and Daniel Ueltschi

Abstract

We investigate the typical cycle lengths, the total number of cycles, and the number of finite cycles in random permutations whose probability involves cycle weights. Typical cycle lengths and total number of cycles depend strongly on the parameters, while the distributions of finite cycles are usually independent Poisson random variables.Comment: 22 pages, 2 figure

Topics: Mathematics - Probability, Mathematics - Combinatorics, 60K35
Year: 2012
DOI identifier: 10.1002/rsa.20430
OAI identifier: oai:arXiv.org:1102.4796
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