Global regime for general additive functionals of conditioned Bienayme-Galton-Watson trees

• 成果类型: Article
• 署名作者: Abraham, Romain; Delmas, Jean-Francois; Nassif, Michel
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Orleans; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01095-9
• 发表日期: 2022
• 页码: 277-351
• 关键词: scaling limits; levy; parameters; THEOREM; shape

摘要

We give an invariance principle for very general additive functionals of conditioned Bienayme-Galton-Watson trees in the global regime when the offspring distribution lies in the domain of attraction of a stable distribution, the limit being an additive functional of a stable Levy tree. This includes the case when the offspring distribution has finite variance (the Levy tree being then the Brownian tree). We also describe, using an integral test, a phase transition for toll functions depending on the size and height.