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

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

2007-04-24

arxiv.org/abs/0704.3122v1

Mathematics

Probability

Scientific paper

We show that for $0<\alpha<1$ and $\theta>-\alpha$, the Poisson-Dirichlet
distribution with parameter $(\alpha, \theta)$ 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 $\alpha =0$.

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