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Random permutations of a regular lattice
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Betz, Volker (2014) Random permutations of a regular lattice. Journal of Statistical Physics, Volume 155 (Number 6). pp. 1222-1248. doi:10.1007/s10955-014-0945-7 ISSN 0022-4715.
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Official URL: http://dx.doi.org/10.1007/s10955-014-0945-7
Abstract
Spatial random permutations were originally studied due to their connections to Bose–Einstein condensation, but they possess many interesting properties of their own. For random permutations of a regular lattice with periodic boundary conditions, we prove existence of the infinite volume limit under fairly weak assumptions. When the dimension of the lattice is two, we give numerical evidence of a Kosterlitz–Thouless transition, and of long cycles having an almost sure fractal dimension in the scaling limit. Finally we comment on possible connections to Schramm–Löwner curves.
Item Type: | Journal Article | ||||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||
Journal or Publication Title: | Journal of Statistical Physics | ||||||||||
Publisher: | Springer New York LLC | ||||||||||
ISSN: | 0022-4715 | ||||||||||
Official Date: | June 2014 | ||||||||||
Dates: |
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Volume: | Volume 155 | ||||||||||
Number: | Number 6 | ||||||||||
Page Range: | pp. 1222-1248 | ||||||||||
DOI: | 10.1007/s10955-014-0945-7 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access |
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