Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees

• 成果类型: Article
• 署名作者: Aldous, D; Miermont, G; Pitman, J
• 署名单位: University of California System; University of California Berkeley; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0407-2
• 发表日期: 2005
• 页码: 1-17
• 关键词: brownian bridge asymptotics

摘要

We study the asymptotics of the p-mapping model of random mappings on [n] as n gets large, under a large class of asymptotic regimes for the underlying distribution p. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2004) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite number of attracting points to emerge.