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


 
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1. Title Title of document Asymptotics of Certain Coagulation-Fragmentation Processes and Invariant Poisson-Dirichlet Measures
 
2. Creator Author's name, affiliation, country Eddy Mayer-Wolf; Technion
 
2. Creator Author's name, affiliation, country Ofer Zeitouni; Technion
 
2. Creator Author's name, affiliation, country Martin P.W. Zerner; Stanford University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Partitions, coagulation, fragmentation, invariant measures, Poisson-Dirichlet.
 
3. Subject Subject classification 60K35
 
4. Description 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.
 
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7. Date (YYYY-MM-DD) 2002-02-14
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/107
 
10. Identifier Digital Object Identifier 10.1214/EJP.v7-107
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 7
 
12. Language English=en
 
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