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Two-Parameter Poisson–Dirichlet Measures and Reversible Exchangeable Fragmentation–Coalescence Processes

Published online by Cambridge University Press:  01 May 2008

JEAN BERTOIN*
Affiliation:
Laboratoire de Probabilités, Université Pierre et Marie Curie and DMA, Ecole Normale Supérieure, 45, rue d'Ulm, F-75005 Paris, France (e-mail: [email protected])

Abstract

We show that for 0<α<1 and θ>−α, the Poisson–Dirichlet distribution with parameter (α, θ) is the unique reversible distribution of a rather natural fragmentation–coalescence process. This completes earlier results in the literature for certain split-and-merge transformations and the parameter α = 0.

Type
Paper
Copyright
Copyright © Cambridge University Press 2007

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