Random Walk on a Randomly Oriented Honeycomb Lattice

#### G. Bosi, M. Campanino

2019, v.25, Issue 1, 75-99

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 (\hspace{-0.1pt}\cite{ref1}, \cite{ref2}).
%Due to the lack of independence of the vertical and horizontal motions of the random walk new techniques are developed to prove the results.

Keywords: Markov chain, random environment, random graph, honeycomb lattice, hexagonal lattice, recurrence criteria, directed graph