Two-parameter Poisson-Dirichlet measures and reversible exchangeable fragmentation-coalescence processes

2007/04/24 by Bertoin, Jean
#60 J 25 #60 J 27 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0704.3122

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.

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