Partition structures derived from Brownian motion and stable subordinators

@article{Pitman1997PartitionSD,
  title={Partition structures derived from Brownian motion and stable subordinators},
  author={Jim Pitman},
  journal={Bernoulli},
  year={1997},
  volume={3},
  pages={79-96}
}
  • J. Pitman
  • Published 1 March 1997
  • Mathematics
  • Bernoulli
Explicit formulae are obtained for the distribution of various random partitions of a positive integer n, both ordered and unordered, derived from the zero set M of a Brownian motion by the following scheme: pick n points uniformly at random from [0, 1], and classify them by whether they fall in the same or different component intervals of the complement of M. Corresponding results are obtained for M the range of a stable subordinator and for bridges defined by conditioning on 1 E M. These… 
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