Friday, April 27, 2012

1007.2224 (Volker Betz et al.)

Spatial random permutations and Poisson-Dirichlet law of cycle lengths    [PDF]

Volker Betz, Daniel Ueltschi
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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