Work

Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

Year: 2008

Type: article

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.

Source: The Annals of Probability

DOI: 10.1214/07-aop377

Authors: Bénédicte Haas, Grégory Miermont, Jim Pitman, Matthias Winkel

Institutions: Université Paris Dauphine-PSL, University of Oxford

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Engineering and Physical Sciences Research Council

Awards: Brownian Motion and Combinatorial Stochastic Processes, G7689814038