Spinal Partitions and Invariance under Re-rooting of Continuum Random Trees

@inproceedings{Pitman2007SpinalPA,
  title={Spinal Partitions and Invariance under Re-rooting of Continuum Random Trees},
  author={Jim Pitman and Matthias Winkel},
  year={2007}
}
We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson–Dirichlet family of continuous fragmentation trees, including the stable trees of Duquesne and Le Gall, the fine partition is obtained from the coarse one by shattering each of its parts independently, according to the same law. As a second… CONTINUE READING
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