Lattice permutations and Poisson-Dirichlet distribution of cycle lengths

Details Lattice permutations and Poisson-Dirichlet distribution of cycle lengths Lattice permutations and Poisson-Dirichlet distribution of cycle lengths

2011-07-26

arxiv.org/abs/1107.5215v2

J. Statist. Phys. 146, 1105-1121 (2012)

Physics

Condensed Matter

Statistical Mechanics

18 pages, 14 figures

Scientific paper

10.1007/s10955-012-0450-9

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.

Affiliated with

Also associated with

No associations

Rating

Lattice permutations and Poisson-Dirichlet distribution of cycle lengths does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Lattice permutations and Poisson-Dirichlet distribution of cycle lengths, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lattice permutations and Poisson-Dirichlet distribution of cycle lengths will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-93742