Open Access
2022 Recurrence and windings of two revolving random walks
Gianluca Bosi, Yiping Hu, Yuval Peres
Author Affiliations +
Electron. J. Probab. 27: 1-22 (2022). DOI: 10.1214/22-EJP781


We study the winding behavior of random walks on two oriented square lattices. One common feature of these walks is that they are bound to revolve clockwise. We also obtain quantitative results of transience/recurrence for each walk.

Funding Statement

GB is supported by a Marco Polo grant from University of Bologna. YH is partially supported by a Gloria Hewitt Fellowship and a McFarlan Fellowship from University of Washington.


We would like to thank anonymous referees whose comments have greatly improved this manuscript. In particular, one referee found out that the normalizing constant in Theorem 1.3 has a very simple form. Another referee pointed out the important reference [6] to us. We are grateful to both of them. We also thank Krzysztof Burdzy and Christopher Hoffman for useful conversations.


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Gianluca Bosi. Yiping Hu. Yuval Peres. "Recurrence and windings of two revolving random walks." Electron. J. Probab. 27 1 - 22, 2022.


Received: 29 September 2021; Accepted: 13 April 2022; Published: 2022
First available in Project Euclid: 17 May 2022

Digital Object Identifier: 10.1214/22-EJP781

Primary: 60G50 , 60J10

Keywords: Lyapunov function , oriented lattices , transience/recurrence , winding

Vol.27 • 2022
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