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.

View original: http://arxiv.org/abs/1007.2224