THE FIXATION LINE IN THE Λ-COALESCENT

• 成果类型: Article
• 署名作者: Henard, Olivier
• 署名单位: University of London; Queen Mary University London
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1077
• 发表日期: 2015
• 页码: 3007-3032
• 关键词: hitting probabilities; beta; length; trees

摘要

We define a Markov process in a forward population model with backward genealogy given by the Lambda-coalescent. This Markov process, called the fixation line, is related to the block counting process through its hitting times. Two applications are discussed. The probability that the n-coalescent is deeper than the (n - 1)-coalescent is studied. The distribution of the number of blocks in the last coalescence of the n-Beta(2 - alpha, alpha)-coalescent is proved to converge as n -> infinity, and the generating function of the limiting random variable is computed.