Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

Details Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

2006-04-15

arxiv.org/abs/math/0604350v2

Annals of Probability 2008, Vol. 36, No. 5, 1790-1837

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP377 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/07-AOP377

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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