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.
- Pub Date:
- July 2010
- Mathematics - Probability;
- Mathematical Physics;
- 20 pages, 1 figure. We are grateful to Antal Jarai for pointing out some omissions in our original proofs, and this version contains an addendum with clarifications. We make two additional assumptions on the jump function. The main results are still valid