Random Walks on Randomly Oriented Lattices,
2003, v.9, Issue 3, 391-412
Simple random walks on various types of partially horizontally oriented regular lattices are considered. The horizontal orientations of the lattices can be of various types (deterministic or random) and depending on the nature of the orientation the asymptotic behaviour of the random walk is shown to be recurrent or transient. In particular, for randomly horizontally oriented lattices the random walk is almost surely transient.
Keywords: Markov chain,random environment,recurrence criteria,random graphs,oriented graphs