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A Consistent Markov Partition Process Generated from the Paintbox Process

  • Harry Crane (a1)

Abstract

We study a family of Markov processes on P (k), the space of partitions of the natural numbers with at most k blocks. The process can be constructed from a Poisson point process on R + x ∏ i=1 k P (k) with intensity dt ⊗ ϱν (k), where ϱν is the distribution of the paintbox based on the probability measure ν on P m, the set of ranked-mass partitions of 1, and ϱν (k) is the product measure on ∏ i=1 k P (k). We show that these processes possess a unique stationary measure, and we discuss a particular set of reversible processes for which transition probabilities can be written down explicitly.

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Copyright

Corresponding author

Postal address: Department of Statistics, University of Chicago, Eckhart Hall Room 108, 5734 South University Avenue, Chicago, IL 60637, USA. Email address: crane@uchicago.edu

References

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A Consistent Markov Partition Process Generated from the Paintbox Process

  • Harry Crane (a1)

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