Poisson-Kingman partitions

Jim Pitman

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Poisson-Kingman partitions

Jim Pitman

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Abstract

This paper presents some general formulas for random partitions of a finite set derived by Kingman's model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the two-parameter family of Poisson-Dirichlet models derived from the Poisson process of jumps of a stable subordinator. Applications are made to the random partition generated by the lengths of excursions of a Brownian motion or Brownian bridge conditioned on its local time at zero.

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Jim Pitman. 2002-10-24. Poisson-Kingman partitions. https://arxiv.org/abs/math/0210396

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