Favorite sites for simple random walk in two and more dimensions
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- DOI码：10.1007/s00440-025-01441-1
- 发表刊物：Probability Theory and Related Fields
- 关键字：Random walk, Local time, Favorite site
- 摘要：On the trace of a discrete-time simple random walk on $\mathbb{Z}^d$ for $d\geq 2$, we consider the evolution of favorite sites, i.e., sites that achieve the maximal local time at a certain time. For $d=2$, we show that almost surely three favorite sites occur simultaneously infinitely often and eventually there is no simultaneous occurrence of four favorite sites. For $d\geq 3$, we derive sharp asymptotics of the number of favorite sites. This answers an open question of Erd\H{o}s and R\'{e}v\'{e}sz (1984), which was brought up again by Dembo (2005).
- 第一作者：Chenxu Hao, Xinyi Li, Izumi Okada, Zheng Yushu
- 论文类型：期刊论文
- 学科门类：理学
- 一级学科：数学
- 是否译文：否
- 发表时间：2025-11-12
- 收录刊物：SCI
附件：
25-HLOZ.pdf
