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Spatial random permutations and Poisson-Dirichlet law of cycle lengths

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Betz, Volker and Ueltschi, Daniel (2011) Spatial random permutations and Poisson-Dirichlet law of cycle lengths. Electronic Journal of Probability, Vol.16 (No.41).

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Abstract

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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Permutations
Journal or Publication Title: Electronic Journal of Probability
Publisher: University of Washington. Dept. of Mathematics
ISSN: 1083-6489
Official Date: 6 June 2011
Dates:
DateEvent
6 June 2011Published
Volume: Vol.16
Number: No.41
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
Funder: Engineering and Physical Sciences Research Council (EPSRC)
Grant number: EP/D07181X/1 (EPSRC), EP/G056390/1 (EPSRC)
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