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 Electronic Journal of Probability > Vol. 7 (2002) > Paper 8 open journal systems 


Asymptotics of Certain Coagulation-Fragmentation Processes and Invariant Poisson-Dirichlet Measures

Eddy Mayer-Wolf, Technion
Ofer Zeitouni, Technion
Martin P.W. Zerner, Stanford University


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.
Full text: PDF

Pages: 1-25

Published on: February 14, 2002
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Electronic Journal of Probability. ISSN: 1083-6489