Combinatorics, Probability and Computing

Table of Contents - 2008 - Volume 17, Issue 03  

Paper

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

JEAN BERTOINa1

a1 Laboratoire de Probabilités, Université Pierre et Marie Curie and DMA, Ecole Normale Supérieure, 45, rue d'Ulm, F-75005 Paris, France (e-mail: jbe@ccr.jussieu.fr)

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.

(Received April 24 2007)

(Revised October 07 2007)