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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| Published in | Journal of statistical physics Vol. 155; no. 6; pp. 1222 - 1248 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.06.2014
Springer |
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| Online Access | Get full text |
| ISSN | 0022-4715 1572-9613 |
| DOI | 10.1007/s10955-014-0945-7 |
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| 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. |
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| AbstractList | 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-Lowner curves. Keywords Random permutations * Infinite volume limit * Kosterlitz-Thouless transition * Fractal dimension * Schramm-Lowner evolution Mathematics Subject Classification 28A80 * 60K35 * 60D05 * 82B26 * 82B80 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. |
| Audience | Academic |
| Author | Betz, Volker |
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| Cites_doi | 10.1016/j.aop.2005.04.001 10.1088/0305-4470/35/33/303 10.1103/PhysRevLett.39.1201 10.1007/BF01208273 10.1007/s10955-007-9410-1 10.1007/BF02803524 10.1103/PhysRev.91.1291 10.4007/annals.2012.176.3.8 10.1007/s00220-008-0584-4 10.1214/07-AOP364 10.1007/s10955-010-9988-6 10.1103/PhysRevLett.97.170601 10.1088/0305-4470/26/18/031 10.1090/S0002-9947-2010-04964-5 10.1007/s00440-009-0248-0 10.1214/aop/1079021469 10.1088/0022-3719/6/7/010 10.1007/s10955-012-0450-9 10.1002/0470013850 10.1016/S0764-4442(01)01991-7 10.1214/EJP.v16-901 10.1103/PhysRevLett.17.1307 |
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| Keywords | Infinite volume limit 60D05 82B26 Fractal dimension Kosterlitz–Thouless transition 28A80 Schramm–Löwner evolution 60K35 82B80 Random permutations |
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| Snippet | Spatial random permutations were originally studied due to their connections to Bose–Einstein condensation, but they possess many interesting properties of... Spatial random permutations were originally studied due to their connections to Bose-Einstein condensation, but they possess many interesting properties of... |
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| SubjectTerms | Mathematical and Computational Physics Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical |
| Title | Random Permutations of a Regular Lattice |
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