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July 2009 Spinal partitions and invariance under re-rooting of continuum random trees
Bénédicte Haas, Jim Pitman, Matthias Winkel
Ann. Probab. 37(4): 1381-1411 (July 2009). DOI: 10.1214/08-AOP434


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 application of spinal decompositions, we prove that among the continuous fragmentation trees, stable trees are the only ones whose distribution is invariant under uniform re-rooting.


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Bénédicte Haas. Jim Pitman. Matthias Winkel. "Spinal partitions and invariance under re-rooting of continuum random trees." Ann. Probab. 37 (4) 1381 - 1411, July 2009.


Published: July 2009
First available in Project Euclid: 21 July 2009

zbMATH: 1181.60128
MathSciNet: MR2546748
Digital Object Identifier: 10.1214/08-AOP434

Primary: 60J80

Keywords: Continuum random tree , discrete tree , Fragmentation process , Markov branching model , Poisson–Dirichlet distribution , random re-rooting , spinal decomposition

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.37 • No. 4 • July 2009
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