Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

• 成果类型: Article
• 署名作者: Haas, Benedicte; Miermont, Gregory; Pitman, Jim; Winkel, Matthias
• 署名单位: Universite PSL; Universite Paris-Dauphine; Universite Paris Saclay; University of California System; University of California Berkeley; University of Oxford
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP377
• 发表日期: 2008
• 页码: 1790-1837
• 关键词: self-similar fragmentations; LAWS

摘要

Given any regularly varying dislocation we 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. 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 row at the same speed as the mean height of a randomly chosen leaf.