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Lattice permutations and Poisson-Dirichlet distribution of cycle lengths
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Grosskinsky, Stefan, Lovisolo, Alexander A. and Ueltschi, Daniel (2012) Lattice permutations and Poisson-Dirichlet distribution of cycle lengths. Journal of Statistical Physics, Vol.146 (No.6). pp. 1105-1121. doi:10.1007/s10955-012-0450-9 ISSN 0022-4715.
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WRAP_Grosskinsky_Lattice_1107.5215v2.pdf - Accepted Version - Requires a PDF viewer. Download (780Kb) |
Official URL: http://dx.doi.org/10.1007/s10955-012-0450-9
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 Poisson-Dirichlet. This can be explained heuristically using a stochastic coagulation-fragmentation process for long cycles, which is supported by numerical data.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Permutations | ||||
Journal or Publication Title: | Journal of Statistical Physics | ||||
Publisher: | Springer | ||||
ISSN: | 0022-4715 | ||||
Official Date: | March 2012 | ||||
Dates: |
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Volume: | Vol.146 | ||||
Number: | No.6 | ||||
Page Range: | pp. 1105-1121 | ||||
DOI: | 10.1007/s10955-012-0450-9 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 20 December 2015 | ||||
Date of first compliant Open Access: | 20 December 2015 | ||||
Funder: | Erasmus Mundus (Program), Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | EP/E501311/1 (EPSRC), EP/G056390/1 (EPSRC) |
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