THE COALESCENT STRUCTURE OF UNIFORM AND POISSON SAMPLES FROM MULTITYPE BRANCHING PROCESSES

• 成果类型: Article
• 署名作者: Johnston, Samuel g. g.; Lambert, Amaury
• 署名单位: University of London; King's College London; Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1934
• 发表日期: 2023
• 页码: 4820-4857
• 关键词: genealogy

摘要

We introduce a Poissonization method to study the coalescent structure of uniform samples from branching processes. This method relies on the simple observation that a uniform sample of size k taken from a random set with positive Lebesgue measure may be represented as a mixture of Poisson samples with rate lambda and mixing measure k d lambda/lambda. We develop a multitype analogue of this mixture representation, and use it to characterise the coalescent structure of multitype continuous-state branching processes in terms of random multitype forests. Thereafter we study the small time asymptotics of these random forests, establishing a correspondence between multitype continuous-state branching processes and multitype Lambda-coalescents.