A LIMIT LAW FOR THE MOST FAVORITE POINT OF SIMPLE RANDOM WALK ON A REGULAR TREE

• 成果类型: Article
• 署名作者: Biskup, Marek; Louidor, Oren
• 署名单位: University of California System; University of California Los Angeles; Technion Israel Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1644
• 发表日期: 2024
• 页码: 502-544
• 关键词: planar brownian-motion; extremal process; level sets; maximum; CONVERGENCE; minimum; times

摘要

We consider a continuous-time random walk on a regular tree of finite depth and study its favorite points among the leaf vertices. For the walk started from a leaf vertex and stopped upon hitting the root, we prove that, in the limit as the depth of the tree tends to infinity, the suitably scaled and centered maximal time spent at any leaf converges to a randomly-shifted Gumbel law. The random shift is characterized using a derivative-martingale like object associated with square-root local-time process on the tree.