Coagulation-fragmentation duality, Poisson-Dirichlet distributions and random recursive trees (Q997399)

This paper deals with a new approach regarding the duality between fragmentation and coagulation operators and processes in the case of certain Poisson-Dirichlet distributions. After presenting the main definitions and results about the Poisson-Dirichlet distributions and the fragmentation/coagulation operators/processes, the authors focus on a random recursive tree model, encoding the fragmentation process, and give an alternative proof of the above duality. Finally, a discussion concerning the relationship between the recursive tree model and the ``Chinese restaurant process'' in terms of continuous-time branching processes is also presented.