Reinforced Galton-Watson processes III: Empirical offspring distributions

• 成果类型: Article; Early Access
• 署名作者: Bertoin, Jean; Mallein, Bastien
• 署名单位: University of Zurich; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01436-y
• 发表日期: 2025
• 关键词: branching-processes; multitype; CONVERGENCE; THEOREM

摘要

Reinforced Galton-Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forbearers can be repeated randomly by descendants. More specifically, the evolution depends on the empirical offspring distribution of each individual along its ancestral lineage. We are interested here in asymptotic properties of the empirical distributions observed in the population, such as concentration, evanescence and persistence. For this, we incorporate tools from the theory of large deviations to our preceding analysis [4, 5].