Poisson-Kingman partitions

Details Poisson-Kingman partitions Poisson-Kingman partitions

2002-10-24

arxiv.org/abs/math/0210396v1

Mathematics

Probability

34 pages

Scientific paper

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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