  We consider recurrent diffusive random walks on a strip. We present
constructive conditions on Green functions of finite sub-domains which imply a
Central Limit Theorem with polynomial error bound, a Local Limit Theorem, and
mixing of environment viewed by the particle process. Our conditions can be
verified for a wide class of environments including independent environments,
quasiperiodic environments, and environments which are asymptotically constant
at infinity. The conditions presented deal with a fixed environment, in
particular, no stationarity conditions are imposed.
