Favorite sites of one-dimensional asymmetric simple random walk

Guangshuo Zhou; Zechun Hu; Renming Song

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arXiv · 2511.02316

Favorite sites of one-dimensional asymmetric simple random walk

Guangshuo Zhou·Zechun Hu·Renming Song

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Abstract

In this paper, we study favorite sites of one-dimensional asymmetric simple random walks. We show that almost surely, for any fixed integer $r\geq 1$, ``$r$ favorite sites" occurs infinitely often. We also give the asymptotic growth rate of the number of favorite sites.

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Guangshuo Zhou, Zechun Hu, Renming Song. 2025-11-04. Favorite sites of one-dimensional asymmetric simple random walk. https://arxiv.org/abs/2511.02316

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