English

Poisson representation of a Ewens fragmentation process

Probability 2007-05-23 v1 Combinatorics

Abstract

A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of [n]={1,...,n}[n]=\{1,...,n\} at time θ0\theta \ge 0 is governed by the Ewens sampling formula with parameter θ\theta. These partition-valued processes are exchangeable and consistent, as nn varies. They can be derived by uniform sampling from a corresponding mass fragmentation process defined by cutting a unit interval at the points of a Poisson process with intensity θx1\diffx\theta x^{-1} \diff x on R+{\mathbb R}_+, arranged to be intensifying as θ\theta increases.

Keywords

Cite

@article{arxiv.math/0608307,
  title  = {Poisson representation of a Ewens fragmentation process},
  author = {Alexander Gnedin and Jim Pitman},
  journal= {arXiv preprint arXiv:math/0608307},
  year   = {2007}
}

Comments

10 pages

R2 v1 2026-07-22T17:40:34.361Z