  We study random spatial permutations on Z^3 where each jump x -> \pi(x) is
penalized by a factor exp(-T ||x-\pi(x)||^2). The system is known to exhibit a
phase transition for low enough T where macroscopic cycles appear. We observe
that the lengths of such cycles are distributed according to Poisson-Dirichlet.
This can be explained heuristically using a stochastic
coagulation-fragmentation process for long cycles, which is supported by
numerical data.
