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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
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: jbe@ccr.jussieu.fr)
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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
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 3 , May 2008 , pp. 329 - 337
Copyright
Copyright © Cambridge University Press 2007

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