@article{EJP107,
author = {Eddy Mayer-Wolf and Ofer Zeitouni and Martin Zerner},
title = {Asymptotics of Certain Coagulation-Fragmentation Processes and Invariant Poisson-Dirichlet Measures},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {7},
year = {2002},
keywords = {Partitions, coagulation, fragmentation, invariant measures, Poisson-Dirichlet.},
abstract = {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.},
pages = {no. 8, 1-25},
issn = {1083-6489},
doi = {10.1214/EJP.v7-107},
url = {http://ejp.ejpecp.org/article/view/107}}