Spinal partitions and invariance under re-rooting of continuum random trees
Winkel, Matthias; Pitman, Jim; Haas, Bénédicte (2009), Spinal partitions and invariance under re-rooting of continuum random trees, Annals of Probability, 37, 4, p. 1381-1411. http://dx.doi.org/10.1214/08-AOP434
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00149050/en/
Journal nameAnnals of Probability
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Abstract (EN)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.
Subjects / Keywordsrandom re-rooting; spinal decomposition; continuum random tree; fragmentation process; Poisson-Dirichlet distribution; discrete tree; Markov branching model
Showing items related by title and author.
Winkel, Matthias; Pitman, Jim; Miermont, Grégory; Haas, Bénédicte (2008-09) Article accepté pour publication ou publié