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Open Access
2007 A dynamical characterization of Poisson-Dirichlet distributions
Louis-Pierre Arguin
Author Affiliations +
Electron. Commun. Probab. 12: 283-290 (2007). DOI: 10.1214/ECP.v12-1300

Abstract

We show that a slight modification of a theorem of Ruzmaikina and Aizenman on competing particle systems on the real line leads to a characterization of Poisson-Dirichlet distributions PD(α,0). Precisely, let ξ be a proper random mass-partition i.e. a random sequence (ξi,iN) such that ξ1ξ20 and iξi=1 a.s. Consider {Wi}iN, an iid sequence of random positive numbers whose distribution is absolutely continuous with respect to the Lebesgue measure and E[Wλ]< for all λR. It is shown that, if the law of ξ is invariant under the random reshuffling (ξi,iN)(ξiWijξjWj,iN) where the weights are reordered after evolution, then it must be a mixture of Poisson-Dirichlet distributions PD(α,0),α.

Citation

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Louis-Pierre Arguin. "A dynamical characterization of Poisson-Dirichlet distributions." Electron. Commun. Probab. 12 283 - 290, 2007. https://doi.org/10.1214/ECP.v12-1300

Information

Accepted: 21 September 2007; Published: 2007
First available in Project Euclid: 6 June 2016

zbMATH: 1128.60037
MathSciNet: MR2342707
Digital Object Identifier: 10.1214/ECP.v12-1300

Subjects:
Primary: 60G55
Secondary: 60G57

Keywords: Point processes , Poisson-Dirichlet distributions

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