Three favorite sites occurs infinitely often for one-dimensional simple random walk

Authors
Ding, Jian Shen, Jianfei
Citation
Ding, Jian et Shen, Jianfei, Three favorite sites occurs infinitely often for one-dimensional simple random walk, Annals of probability (Online) , 46(5), 2018, pp. 2545-2561
Journal title
Annals of probability (Online) → ACNP
ISSN journal
2168894X
Volume
46
Issue
5
Year of publication
2018
Pages
2545 - 2561
Database
ACNP
SICI code
Abstract
For a one-dimensional simple random walk (St), 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 Tóth [Ann. Probab. 29 (2001) 484.503], and disproves a conjecture of Erd.s and Révész [In Mathematical Structure.Computational Mathematics.Mathematical Modelling 2 (1984) 152.157] and of Tóth [Ann. Probab. 29 (2001) 484.503].