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

Abstract

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.