A FUNCTIONAL LIMIT THEOREM FOR THE PROFILE OF b-ARY TREES

• 成果类型: Article
• 署名作者: Schopp, Eva-Maria
• 署名单位: University of Freiburg
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP640
• 发表日期: 2010
• 页码: 907-950
• 关键词: random recursive trees; large deviations; weighted height; CONVERGENCE; martingales; numbers; width

摘要

In this paper we prove a functional limit theorem for the weighted profile of a b-ary tree. For the proof we use classical martingales connected to branching Markov processes and a generalized version of the profile-polynomial martingale. By embedding, choosing weights and a branch factor in a right way, we finally rediscover the profiles of some well-known discrete time trees.