Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

Bénédicte Haas, Grégory Miermont, Jim Pitman, Matthias Winkel

Published 2006-04-15, updated 2008-09-25Version 2

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.