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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.

MSC:

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
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References:

[1] DOI: 10.1007/BF02785366 · Zbl 1130.60302
[2] DOI: 10.1137/S0040585X97977331 · Zbl 0960.60012
[3] DOI: 10.1214/aop/1024404422 · Zbl 0880.60076
[4] DOI: 10.1017/S0963548302005163 · Zbl 1011.60051
[5] DOI: 10.1017/S0963548301004692 · Zbl 0976.62008
[6] DOI: 10.1214/aop/1022677552 · Zbl 0963.60079
[7] DOI: 10.1002/rsa.20020 · Zbl 1060.60020
[8] DOI: 10.1007/BF01205234 · Zbl 0741.60037
[9] DOI: 10.1023/A:1021682212351 · Zbl 0930.60094
[10] DOI: 10.1214/aop/1015345761 · Zbl 1013.92029
[11] DOI: 10.1214/aop/1079021468 · Zbl 1049.60088
[12] Bertoin, Random Fragmentation and Coagulation Processes (2006) · Zbl 1107.60002
[13] Kelly, Reversibility and Stochastic Networks (1979)
[14] DOI: 10.1007/s004400100152 · Zbl 0992.60076
[15] Basdevant, Markov Process. Rel. Fields 12 pp 447– (2006)
[16] Arratia, Logarithmic Combinatorial Structures: A Probabilistic Approach (2003)
[17] Whittle, Systems in Stochastic Equilibrium (1986)
[18] DOI: 10.1239/jap/1032374759 · Zbl 0962.92026
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