A study of random walks on wedges

TL;DR

This paper investigates random walks on wedge-shaped graphs, providing a criterion for recurrence and transience, and establishing that wedges have infinite collision properties if and only if they are recurrent.

Contribution

It introduces a simple recurrence criterion for random walks on wedges and links the infinite collision property directly to recurrence.

Findings

Wedges are recurrent if and only if they have the infinite collision property.

A simple criterion for recurrence and transience of random walks on wedges.

Wedges with certain structures exhibit infinite collisions if recurrent.

Abstract

In this paper we develop the idea of Lyons and gives a simple criterion for the recurrence and the transience. We also show that a wedge has the infinite collision property if and only if it is a recurrent graph.