Random Permutations of a Regular Lattice

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...

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Bibliographic Details
Published inJournal of statistical physics Vol. 155; no. 6; pp. 1222 - 1248
Main Author Betz, Volker
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.06.2014
Springer
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Infinite volume limit
60D05
82B26
Fractal dimension
Kosterlitz–Thouless transition
28A80
Schramm–Löwner evolution
60K35
82B80
Random permutations
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ISSN0022-4715
1572-9613
DOI10.1007/s10955-014-0945-7

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Summary: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.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-014-0945-7