Two-parameter Poisson-Dirichlet measures and reversible exchangeable fragmentation-coalescence processes. (English) Zbl 1165.60032

The paper deals with exchangeable fragmentation-coagulation processes. These processes are models for phenomena of fragmentation and coagulation that can be observed in many sciences and at a great variety of scales – from, for example, DNA fragmentation to formation of planets by accretion. In this paper, the author proves that the two-parameter Poisson-Dirichlet distribution is the unique reversible measure of a rather natural fragmentation-coagulation process.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J25 Continuous-time Markov processes on general state spaces
60J27 Continuous-time Markov processes on discrete state spaces
Full Text: DOI arXiv


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