Recurrence and windings of two revolving random walks

TL;DR

This paper investigates the winding patterns of two specific revolving random walks on oriented square lattices, providing insights into their clockwise behavior and their transience or recurrence properties.

Contribution

It introduces a detailed analysis of the winding behavior and transience/recurrence characteristics of two novel revolving random walks on lattices.

Findings

Both walks exhibit clockwise winding behavior.

Quantitative criteria for transience and recurrence are established.

The walks demonstrate distinct winding and recurrence properties.

Abstract

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.