Asymptotics of certain coagulation-fragmentation processes and invariant Poisson-Dirichlet measures
| dc.creator | Mayer-Wolf, Eddy | |
| dc.creator | Zeitouni, Ofer | |
| dc.creator | Zerner, Martin P. W. | |
| dc.date | 2001-05-13 | |
| dc.date.accessioned | 2026-07-07T04:41:41Z | |
| dc.date.available | 2026-07-07T04:41:41Z | |
| dc.description | 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 $β_m$ (if the sampled parts are distinct) or splitting the part with probability $β_s$ according to a law $σ$ (if the same part was sampled twice). We characterize invariant probability measures for such chains. In particular, if $σ$ 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. | |
| dc.identifier | https://arxiv.org/abs/math/0105111 | |
| dc.identifier | http://arxiv.org/abs/math/0105111 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61464 | |
| dc.subject | Probability | |
| dc.subject | 60K35; 60J27; 60G55 | |
| dc.title | Asymptotics of certain coagulation-fragmentation processes and invariant Poisson-Dirichlet measures | |
| dc.type | text |