# 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 $\alpha =0$.

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 $\alpha =0$.

## Citations

6 citations in Web of Science®
5 citations in Scopus®

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 2008 29 May 2013 15:30 05 Apr 2016 16:47 Cambridge University Press 0963-5483 https://doi.org/10.1017/S0963548307008784 http://www.ams.org/mathscinet-getitem?mr=2410390http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1165.60032http://arxiv.org/abs/0704.3122
Permanent URL: https://doi.org/10.5167/uzh-78180

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