Random Permutations of a Regular Lattice

@article{Betz2013RandomPO,
  title={Random Permutations of a Regular Lattice},
  author={Volker Betz},
  journal={Journal of Statistical Physics},
  year={2013},
  volume={155},
  pages={1222-1248}
}
  • V. Betz
  • Published 11 September 2013
  • Mathematics
  • Journal of Statistical Physics
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… 
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