Random walk on a randomly oriented honeycomb lattice

TL;DR

This paper investigates how random walks behave on honeycomb lattices with randomly oriented edges, showing conditions for recurrence and transience, extending previous results from square grid lattices.

Contribution

It provides new insights into recurrence and transience of random walks on honeycomb lattices with random orientations, expanding the understanding beyond square grid cases.

Findings

Conditions for almost sure recurrence

Conditions for almost sure transience

Extension of previous lattice results

Abstract

We study the recurrence behaviour of random walks on partially oriented honeycomb lattices. The vertical edges are undirected while the orientation of the horizontal edges is random: depending on their distribution, we prove a.s. transience in some cases, and a.s. recurrence in other ones. The results extend those obtained for the partially oriented square grid lattices (Campanino and Petritis (2003), Campanino and Petritis (2014)).