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.
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  to us. We are grateful to both of them. We also thank Krzysztof Burdzy and Christopher Hoffman for useful conversations.
"Recurrence and windings of two revolving random walks." Electron. J. Probab. 27 1 - 22, 2022. https://doi.org/10.1214/22-EJP781