THE POISSON-DIRICHLET LAW IS THE UNIQUE INVARIANT DISTRIBUTION FOR UNIFORM SPLIT-MERGE

We consider a Markov chain 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 (if the sampled parts are distinct) or splitting the part uniformly (if the same part was sampled twice). We prove a...

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Bibliographic Details
Published in:The Annals of probability 2004-01, Vol.32 (1B), p.915
Main Authors: Diaconis, Persi, Mayer-Wolf, Eddy, Zeitouni, Ofer, Zerner, Martin P W
Format: Article
Language:English
Subjects:
Markov analysis
Mathematical models
Studies
Online Access:Get full text
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Summary:We consider a Markov chain 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 (if the sampled parts are distinct) or splitting the part uniformly (if the same part was sampled twice). We prove a conjecture of Vershik stating that the Poisson-Dirchlet law with parameter theta = 1 is the unique invariant distribution for this Markov chain. Our proof uses a combination of probabilistic, combinatoric and representation-theoretic argument. [PUBLICATION ABSTRACT]
ISSN:0091-1798
2168-894X