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We consider recurrent diffusive random walks on a strip. We presentconstructive conditions on Green functions of finite sub-domains which imply aCentral Limit Theorem with polynomial error bound, a Local Limit Theorem, andmixing of environment viewed by the particle process. Our conditions can beverified for a wide class of environments including independent environments,quasiperiodic environments, and environments which are asymptotically constantat infinity. The conditions presented deal with a fixed environment, inparticular, no stationarity conditions are imposed.

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