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.
Publié le : 2008-09-15
Classification:
Markov branching model,
self-similar fragmentation,
continuum random tree,
ℝ-tree,
phylogenetic tree,
60J80
@article{1221138767,
author = {Haas, B\'en\'edicte and Miermont, Gr\'egory and Pitman, Jim and Winkel, Matthias},
title = {Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models},
journal = {Ann. Probab.},
volume = {36},
number = {1},
year = {2008},
pages = { 1790-1837},
language = {en},
url = {http://dml.mathdoc.fr/item/1221138767}
}
Haas, Bénédicte; Miermont, Grégory; Pitman, Jim; Winkel, Matthias. Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models. Ann. Probab., Tome 36 (2008) no. 1, pp. 1790-1837. http://gdmltest.u-ga.fr/item/1221138767/