TIGHTNESS FOR A FAMILY OF RECURSION EQUATIONS

• 成果类型: Article
• 署名作者: Bramson, Maury; Zeitouni, Ofer
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP414
• 发表日期: 2009
• 页码: 615-653
• 关键词: branching random-walk; brownian-motion; height; displacement

摘要

In this paper we study the tightness of solutions for a family of recursion equations. These equations arise naturally in the study of random walks on tree-like structures. Examples include the maximal displacement of a branching random walk in one dimension and the cover time of a symmetric simple random walk on regular binary trees. Recursion equations associated with the distribution functions of these quantities have been used to establish weak laws of large numbers. Here, we use these recursion equations to establish the tightness of the corresponding sequences of distribution functions after appropriate centering. We phrase our results in a fairly general context, which we hope will facilitate their application in other settings.