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Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

Bénédicte Haas·Grégory Miermont·Jim Pitman·Matthias Winkel
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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.

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Bénédicte Haas, Grégory Miermont, Jim Pitman, Matthias Winkel. 2008-09-25. Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models. https://doi.org/10.1214/07-aop377

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