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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). ISSN 1083-6489

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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
Date:	6 June 2011
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)
Related URLs:	Publisher
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URI:	http://wrap.warwick.ac.uk/id/eprint/40040