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Spatial Random Permutations and Poisson-Dirichlet Law of Cycle Lengths

   
@article{EJP901,
	author = {Volker Betz and Daniel Ueltschi},
	title = {Spatial Random Permutations and Poisson-Dirichlet Law of Cycle Lengths},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {16},
	year = {2011},
	keywords = {Spatial random permutations, cycle weights, Poisson-Dirichlet distribution},
	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.},
	pages = {no. 41, 1173-1192},
	issn = {1083-6489},
	doi = {10.1214/EJP.v16-901},    
        url = {http://ejp.ejpecp.org/article/view/901}}