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

Jian Ding; Jianfei Shen

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arXiv · 1612.01983

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

Jian Ding·Jianfei Shen

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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 T\'oth (2001), and disproves a conjecture of Erd\"{o}s and R\'ev\'esz (1984) and of T\'oth (2001).

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Jian Ding, Jianfei Shen. 2016-12-06. Three favorite sites occurs infinitely often for one-dimensional simple random walk. https://arxiv.org/abs/1612.01983

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