Electronic Journal of Probability

Spatial Random Permutations and Poisson-Dirichlet Law of Cycle Lengths

Volker Betz and Daniel Ueltschi

Full-text: Open access

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.

Article information

Source
Electron. J. Probab. Volume 16 (2011), paper no. 41, 1173-1192.

Dates
Accepted: 6 June 2011
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464820210

Digital Object Identifier
doi:10.1214/EJP.v16-901

Mathematical Reviews number (MathSciNet)
MR2820074

Zentralblatt MATH identifier
1231.60108

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B26: Phase transitions (general)

Keywords
Spatial random permutations cycle weights Poisson-Dirichlet distribution

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Betz, Volker; Ueltschi, Daniel. Spatial Random Permutations and Poisson-Dirichlet Law of Cycle Lengths. Electron. J. Probab. 16 (2011), paper no. 41, 1173--1192. doi:10.1214/EJP.v16-901. https://projecteuclid.org/euclid.ejp/1464820210


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