Spatial random permutations and Poisson-Dirichlet law of cycle lengths

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.

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

References in corpus (4)

• Spatial random permutations and infinite cycles
• Random permutations with cycle weights
• Critical Temperature of Dilute Bose Gases
• Shift in critical temperature for random spatial permutations with cycle weights

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