The Annals of Probability

Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

Bénédicte Haas, Grégory Miermont, Jim Pitman, and Matthias Winkel

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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.

Article information

Source
Ann. Probab. Volume 36, Number 5 (2008), 1790-1837.

Dates
First available in Project Euclid: 11 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.aop/1221138767

Digital Object Identifier
doi:10.1214/07-AOP377

Mathematical Reviews number (MathSciNet)
MR2440924

Zentralblatt MATH identifier
1155.92033

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Markov branching model self-similar fragmentation continuum random tree ℝ-tree phylogenetic tree

Citation

Haas, Bénédicte; Miermont, Grégory; Pitman, Jim; Winkel, Matthias. Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models. Ann. Probab. 36 (2008), no. 5, 1790--1837. doi:10.1214/07-AOP377. https://projecteuclid.org/euclid.aop/1221138767


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