Translator Disclaimer
September 2008 Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models
Bénédicte Haas, Grégory Miermont, Jim Pitman, Matthias Winkel
Ann. Probab. 36(5): 1790-1837 (September 2008). DOI: 10.1214/07-AOP377

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.

Citation

Download Citation

Bénédicte Haas. Grégory Miermont. Jim Pitman. Matthias Winkel. "Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models." Ann. Probab. 36 (5) 1790 - 1837, September 2008. https://doi.org/10.1214/07-AOP377

Information

Published: September 2008
First available in Project Euclid: 11 September 2008

zbMATH: 1155.92033
MathSciNet: MR2440924
Digital Object Identifier: 10.1214/07-AOP377

Subjects:
Primary: 60J80

Rights: Copyright © 2008 Institute of Mathematical Statistics

JOURNAL ARTICLE
48 PAGES


SHARE
Vol.36 • No. 5 • September 2008
Back to Top