Poisson-Dirichlet And Gem Invariant Distributions For Split-And-Merge Transformations Of An Interval Partition

@article{Pitman2002PoissonDirichletAG,
  title={Poisson-Dirichlet And Gem Invariant Distributions For Split-And-Merge Transformations Of An Interval Partition},
  author={Jim Pitman},
  journal={Combinatorics, Probability & Computing},
  year={2002},
  volume={11},
  pages={501-514}
}
This paper introduces a split-and-merge transformation of interval partitions which combines some features of one model studied by Gnedin and Kerov [12, 11] and another studied by Tsilevich [30, 31] and Mayer-Wolf, Zeitouni and Zerner [21]. The invariance under this split-and-merge transformation of the interval partition generated by a suitable Poisson process yields a simple proof of the recent result of [21] that a Poisson-Dirichlet distribution is invariant for a closely related… CONTINUE READING
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