Constructive approach to limit theorems for recurrent diffusive random walks on a strip

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