Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models
arXiv:math/0604350 · 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.
Published in at http://dx.doi.org/10.1214/07-AOP377 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
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- Distributions of linear functionals of two parameter Poisson--Dirichlet random measures
- Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions
- Coagulation--fragmentation duality, Poisson--Dirichlet distributions and random recursive trees
- Probabilistic Models for the (sub)Tree(s) of Life
- Regenerative tree growth: Markovian embedding of fragmenters, bifurcators, and bead splitting processes
- Markov branching in the vertex splitting model
- Random tree growth by vertex splitting
- Entropy and Hausdorff Dimension in Random Growing Trees