| Título: | Asymptotics of Certain Coagulation-Fragmentation Processes and Invariant Poisson-Dirichlet Measures |
| Autores: |
Mayer-Wolf, Eddy; Technion Zeitouni, Ofer; Technion Zerner, Martin P.W.; Stanford University |
| Fecha: | 2002-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Partitions, coagulation, fragmentation, invariant measures, Poisson-Dirichlet. 60K35 |
| Descripción: | We consider Markov chains on the space of (countable) partitions of the interval $[0,1]$, obtained first by size biased sampling twice (allowing repetitions) and then merging the parts with probability $\beta_m$ (if the sampled parts are distinct) or splitting the part with probability $\beta_s$, according to a law $\sigma$ (if the same part was sampled twice). We characterize invariant probability measures for such chains. In particular, if $\sigma$ is the uniform measure, then the Poisson-Dirichlet law is an invariant probability measure, and it is unique within a suitably defined class of "analytic" invariant measures. We also derive transience and recurrence criteria for these chains. |
| Idioma: | No aplica |
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