Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models
Bénédicte Haas, Grégory Miermont, Jim Pitman, and Matthias Winkel
Source: Ann. Probab. Volume 36, Number 5 (2008), 1790-1837.
Abstract
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of Aldous’s beta-splitting models and Ford’s alpha models for phylogenetic trees. This confirms in a strong way that the whole trees grow at the same speed as the mean height of a randomly chosen leaf.
Primary Subjects: 60J80
Keywords: Markov branching model; self-similar fragmentation; continuum random tree; ℝ-tree; phylogenetic tree
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1221138767
Digital Object Identifier: doi:10.1214/07-AOP377
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