THE JOINT FLUCTUATIONS OF THE LENGTHS OF THE Beta(2-α, α)-COALESCENTS

• 成果类型: Article
• 署名作者: Birkner, Matthias; Dahmer, Iulia; Diehl, Christina S.; Kersting, Goetz
• 署名单位: Johannes Gutenberg University of Mainz; Goethe University Frankfurt
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1964
• 发表日期: 2024
• 页码: 277-317
• 关键词: lambda-coalescents; weighted sums; branch length; beta; asymptotics; number

摘要

We consider Beta(2 - alpha, alpha)-coalescents with parameter range 1 < alpha < 2 starting from n leaves. The length l(r)((n)) of order r in the n-Beta(2 - alpha, alpha)-coalescent tree is defined as the sum of the lengths of all branches that carry a subtree with r leaves. We show that for any s is an element of N the vector of suitably centered and rescaled lengths of orders 1 <= r <= s converges in distribution to a multivariate stable distribution as the number of leaves tends to infinity.