The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transformations
成果类型：
Article
署名作者：
Diaconis, P; Mayer-Wolf, E; Zeitouni, O; Zerner, MPW
署名单位：
Stanford University; Stanford University; University of Minnesota System; University of Minnesota Twin Cities
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2004
页码：
915-938
关键词：
摘要：
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-Dirichlet 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 arguments.