Betz, Volker and Ueltschi, Daniel. (2011) Spatial random permutations with small cycle weights. Probability Theory and Related Fields, Vol.149 (No.1-2). pp. 191-222. ISSN 0178-8051

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Abstract

We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in the space and there is an additional weight that involves the length of permutation jumps. We prove the occurrence of infinite macroscopic cycles above a certain critical density.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Probability Theory and Related Fields
Publisher:	Springer
ISSN:	0178-8051
Date:	February 2011
Volume:	Vol.149
Number:	No.1-2
Page Range:	pp. 191-222
Identification Number:	10.1007/s00440-009-0248-0
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), US National Science Foundation
Grant number:	EPSRC (EP/D07181X/1), US National Science Foundation (DMS-0601075)
URI:	http://wrap.warwick.ac.uk/id/eprint/41514

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