THE VERTEX-CUT-TREE OF GALTON-WATSON TREES CONVERGING TO A STABLE TREE
成果类型：
Article
署名作者：
Dieuleveut, Daphne
署名单位：
Universite Paris Saclay
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/14-AAP1047
发表日期：
2015
页码：
2215-2262
关键词：
摘要：
We consider a fragmentation of discrete trees where the internal vertices are deleted independently at a rate proportional to their degree. Informally, the associated cut-tree represents the genealogy of the nested connected components created by this process. We essentially work in the setting of Galton-Watson trees with offspring distribution belonging to the domain of attraction of a stable law of index alpha is an element of (1, 2). Our main result is that, for a sequence of such trees T-n conditioned to have size n, the corresponding rescaled cut-trees converge in distribution to the stable tree of index alpha, in the sense induced by the Gromov-Prokhorov topology. This gives an analogue of a result obtained by Bertoin and Miermont in the case of Galion-Watson trees with finite variance.