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Lattice permutations and PoissonDirichlet distribution of cycle lengths
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Grosskinsky, Stefan, Lovisolo, Alexander A. and Ueltschi, Daniel. (2012) Lattice permutations and PoissonDirichlet distribution of cycle lengths. Journal of Statistical Physics, Vol.146 (No.6). pp. 11051121. ISSN 00224715

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Official URL: http://dx.doi.org/10.1007/s1095501204509
Abstract
We study random spatial permutations on ℤ3 where each jump x↦π(x) is penalized by a factor e−T∥x−π(x)∥2 . The system is known to exhibit a phase transition for low enough T where macroscopic cycles appear. We observe that the lengths of such cycles are distributed according to PoissonDirichlet. This can be explained heuristically using a stochastic coagulationfragmentation process for long cycles, which is supported by numerical data.
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:  Journal of Statistical Physics 
Publisher:  Springer 
ISSN:  00224715 
Official Date:  March 2012 
Volume:  Vol.146 
Number:  No.6 
Page Range:  pp. 11051121 
Identification Number:  10.1007/s1095501204509 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
Funder:  Erasmus Mundus (Program), Engineering and Physical Sciences Research Council (EPSRC) 
Grant number:  EP/E501311/1 (EPSRC), EP/G056390/1 (EPSRC) 
References:  [1] M. Aizenman, Geometric analysis of '4 Fields and Ising models, Commun. Math. Phys. 
URI:  http://wrap.warwick.ac.uk/id/eprint/44525 
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