The stable trees are nested

• 成果类型: Article
• 署名作者: Curien, Nicolas; Haas, Benedicte
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); Universite PSL; Universite Paris-Dauphine
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0472-x
• 发表日期: 2013
• 页码: 847-883
• 关键词: self-similar fragmentations; branching-processes; galton-watson

摘要

We show that we can construct simultaneously all the stable trees as a nested family. More precisely, if we prove that hidden inside any -stable tree we can find a version of an -stable tree rescaled by an independent Mittag-Leffler type distribution. This tree can be explicitly constructed by a pruning procedure of the underlying stable tree or by a modification of the fragmentation associated with it. Our proofs are based on a recursive construction due to Marchal which is proved to converge almost surely towards a stable tree.