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

2020/08/25 by Dolgopyat, Dmitry, Goldsheid, Ilya · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2008.11072

Abstract

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.

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