Three favorite sites occurs infinitely often for one-dimensional simple random walk
Probability
2017-10-26 v2
Abstract
For a one-dimensional simple random walk , for each time we say a site 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).
Cite
@article{arxiv.1612.01983,
title = {Three favorite sites occurs infinitely often for one-dimensional simple random walk},
author = {Jian Ding and Jianfei Shen},
journal= {arXiv preprint arXiv:1612.01983},
year = {2017}
}
Comments
18 pages. Version 2 improves exposition, and adopted the journal template