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September 2018 Three favorite sites occurs infinitely often for one-dimensional simple random walk
Jian Ding, Jianfei Shen
Ann. Probab. 46(5): 2545-2561 (September 2018). DOI: 10.1214/17-AOP1232

Abstract

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 Tóth [Ann. Probab. 29 (2001) 484–503], and disproves a conjecture of Erdős and Révész [In Mathematical Structure—Computational Mathematics—Mathematical Modelling 2 (1984) 152–157] and of Tóth [Ann. Probab. 29 (2001) 484–503].

Citation

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Jian Ding. Jianfei Shen. "Three favorite sites occurs infinitely often for one-dimensional simple random walk." Ann. Probab. 46 (5) 2545 - 2561, September 2018. https://doi.org/10.1214/17-AOP1232

Information

Received: 1 March 2017; Revised: 1 September 2017; Published: September 2018
First available in Project Euclid: 24 August 2018

zbMATH: 06964343
MathSciNet: MR3846833
Digital Object Identifier: 10.1214/17-AOP1232

Subjects:
Primary: 60J15, 60J55

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 5 • September 2018
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