Abstract
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.
Citation
Volker Betz. Daniel Ueltschi. "Spatial Random Permutations and Poisson-Dirichlet Law of Cycle Lengths." Electron. J. Probab. 16 1173 - 1192, 2011. https://doi.org/10.1214/EJP.v16-901
Information
