Two-Parameter Poisson–Dirichlet Measures and Reversible Exchangeable Fragmentation–Coalescence Processes
Jean Bertoin · Combinatorics Probability Computing · 2007
We show that for 0−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.