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

  title={Poisson-Dirichlet And Gem Invariant Distributions For Split-And-Merge Transformations Of An Interval Partition},
  author={Jim Pitman},
  journal={Combinatorics, Probability & Computing},
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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Publications referenced by this paper.
Showing 1-10 of 29 references

A surprising Poisson process

  • R. Durrett, V. Limic
  • Preprint. Dept. Math., Cornell Univ.
  • 2001
Highly Influential
4 Excerpts

Stationary random partitions of a natural series

  • N. V. Tsilevich
  • Teor. Veroyatnost. i Primenen., 44(1):55{73
  • 1999
Highly Influential
10 Excerpts

A characterization of GEM distribu- tions via a split-and-merge transformation. Preprint available via http://mouton.stochasik.math.unigoettingen.de/ gnedin/gem.ps

  • A. Gnedin, S. Kerov
  • 2000
Highly Influential
9 Excerpts

The representation of partition structures

  • J.F.C. Kingman
  • J. London Math. Soc., 18:374{380
  • 1978
Highly Influential
10 Excerpts

Deterministic and stochastic models for coalescence (ag- gregation and coagulation): a review of the mean- eld theory for prob- abilists

  • D. J. Aldous
  • Bernoulli, 5:3{48
  • 1999
1 Excerpt

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