SUPERCRITICAL PERCOLATION ON LARGE SCALE-FREE RANDOM TREES

• 成果类型: Article
• 署名作者: Bertoin, Jean; Uribe Bravo, Geronimo
• 署名单位: University of Zurich; Universidad Nacional Autonoma de Mexico
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP988
• 发表日期: 2015
• 页码: 81-103
• 关键词: branching-processes

摘要

We consider Bernoulli bond percolation on a large scale-free tree in the supercritical regime, meaning informally that there exists a giant cluster with high probability. We obtain a weak limit theorem for the sizes of the next largest clusters, extending a recent result in Bertoin [Random Structures Algorithms 44 (2014) 29-44] for large random recursive trees. The approach relies on the analysis of the asymptotic behavior of branching processes subject to rare neutral mutations, which may be of independent interest.