CORRECTION TERMS FOR THE HEIGHT OF WEIGHTED RECURSIVE TREES

• 成果类型: Article
• 署名作者: Pain, Michel; Senizergues, Delphin
• 署名单位: New York University; University of British Columbia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1756
• 发表日期: 2022
• 页码: 3027-3059
• 关键词: convergence

摘要

Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of weights, the first order for the height of such trees has been recently established by one of the authors. In this paper, we obtain the second and third orders in the asymptotic expansion of the height of weighted recursive trees, under similar assumptions. Our methods are inspired from those used to prove similar results for branching random walks. Our results also apply to a related model of growing trees, called the preferential attachment tree with additive fitnesses.