Two-parameter poisson–dirichlet measures and reversible exchangeable fragmentation–coalescence processes

Authors:
Jean Bertoin
Affiliations:
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)
Venue:
Combinatorics, Probability and Computing
Year:
2008

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Abstract

We show that for 0−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.