Two-Parameter Poisson-Dirichlet Measures and Reversible Exchangeable Fragmentation-Coalescence Processes

We show that for 0 < α < 1 and θ > −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. DOI: https://doi.org/10.1017/S0963548307008784 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-78180 Published Version Originally published at: Bertoin, Jean (2008). Two-parameter Poisson-Dirichlet measures and reversible exchangeable fragmentationcoalescence processes. Combinatorics, Probability Computing, 17(3):329-337. DOI: https://doi.org/10.1017/S0963548307008784 Combinatorics, Probability and Computing http://journals.cambridge.org/CPC Additional services for Combinatorics, Probability and Computing: Email alerts: Click here Subscriptions: Click here Commercial reprints: Click here Terms of use : Click here Two­Parameter Poisson–Dirichlet Measures and Reversible Exchangeable Fragmentation–Coalescence Processes