Random walk on a randomly oriented honeycomb lattice

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)).