  We study Markov chains on a lattice in a codimension-one stratified
independent random environment, exploiting results established in [2]. First of
all the random walk is transient in dimension at least three. Focusing on
dimension two, both recurrence and transience can happen, but transience
remains by far the most general situation. We identify the critical scale of
the local drift along the strata corresponding to the frontier between the two
regimes.
