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

Bertoin, Jean (2008). Two-parameter Poisson-Dirichlet measures and reversible exchangeable fragmentation-coalescence processes. Combinatorics, Probability & Computing, 17(3):329-337.

Abstract

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 $\alpha =0$.

Abstract

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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