SPATIAL RANDOM PERMUTATIONS AND POISSON-DIRICHLET LAW OF CYCLE LENGTHS

@inproceedings{Betz2011SPATIALRP,
  title={SPATIAL RANDOM PERMUTATIONS AND POISSON-DIRICHLET LAW OF CYCLE LENGTHS},
  author={Volker Betz and Daniel Ueltschi},
  year={2011}
}
  • Volker Betz, Daniel Ueltschi
  • Published 2011
  • Mathematics, Physics
  • We study spatial permutations with cycle weights that are bounded or slowly diverging. We show that a phase transition occurs at an explicit critical density. The long cycles are macroscopic and their cycle lengths satisfy a Poisson-Dirichlet law. 

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