Spatial random permutations and Poisson-Dirichlet law of cycle lengths

Details Spatial random permutations and Poisson-Dirichlet law of cycle lengths Spatial random permutations and Poisson-Dirichlet law of cycle lengths

2010-07-13

arxiv.org/abs/1007.2224v3

Electr. J. Probab. 16, 1173--1192 (2011)

Mathematics

Probability

20 pages, 1 figure. We are grateful to Antal Jarai for pointing out some omissions in our original proofs, and this version co

Scientific paper

We study spatial permutations with cycle weights that are bounded or slowly
diverging. We show that a phase transition occurs at an explicit critical
density. The long cycles are macroscopic and their cycle lengths satisfy a
Poisson-Dirichlet law.

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