THREE FAVORITE SITES OCCURS INFINITELY OFTEN FOR ONE-DIMENSIONAL SIMPLE RANDOM WALK

• 成果类型: Article
• 署名作者: Ding, Jian; Shen, Jianfei
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1232
• 发表日期: 2018
• 页码: 2545-2561
• 关键词: visited sites; brownian-motion; cover times

摘要

For a one-dimensional simple random walk (S-t), for each time t we say a site x is a favorite site if it has the maximal local time. In this paper, we show that with probability 1 three favorite sites occurs infinitely often. Our work is inspired by Toth [Ann. Probab. 29 (2001) 484-503], and disproves a conjecture of Erdos and Revesz [In Mathematical Structure-Computational Mathematics-Mathematical Modelling 2 (1984) 152-157] and of Toth [Ann. Probab. 29 (2001) 484-503].