Continuum tree asymptotics of discrete fragmentations and applications   to phylogenetic models

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

Winkel, Matthias; Pitman, Jim; Miermont, Grégory; Haas, Bénédicte (2008), Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models, Annals of Probability, 36, 5, p. 1790-1837. http://dx.doi.org/10.1214/07-AOP377

Type

Article accepté pour publication ou publié

External document link

http://fr.arxiv.org/abs/math/0604350

Date

2008-09

Journal name

Annals of Probability

Volume

Number

Publisher

Institute of Mathematical Statistics

Pages

1790-1837

Abstract (EN)

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.

Subjects / Keywords

Markov branching model; self-similar fragmentation; continuum random tree; phylogenetic tree