THE STRUCTURE OF THE ALLELIC PARTITION OF THE TOTAL POPULATION FOR GALTON-WATSON PROCESSES WITH NEUTRAL MUTATIONS

• 成果类型: Article
• 署名作者: Bertoin, Jean
• 署名单位: Sorbonne Universite; Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP441
• 发表日期: 2009
• 页码: 1502-1523
• 关键词: random trees

摘要

We consider a (sub-)critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We specify the law of this allelic partition in terms of the distribution of the number of clone-children and the number of mutant-children of a typical individual. The approach combines an extension of Harris representation of Galton-Watson processes and a version of the ballot theorem. Some limit theorems related to the distribution of the allelic partition arc also given.