Sub-exponential tail bounds for conditioned stable Bienaym,-Galton-Watson trees

• 成果类型: Article
• 署名作者: Kortchemski, Igor
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0704-6
• 发表日期: 2017
• 页码: 1-40
• 关键词: galton-watson trees; critical branching-process; SCALING LIMITS; random-walk; statistics; BEHAVIOR; THEOREM; height; width; MAPS

摘要

We establish uniform sub-exponential tail bounds for the width, height and maximal outdegree of critical Bienaym,-Galton-Watson trees conditioned on having a large fixed size, whose offspring distribution belongs to the domain of attraction of a stable law. This extends results obtained for the height and width by Addario-Berry, Devroye and Janson in the finite variance case.