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.

中文翻译：

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限制带上循环扩散随机游走定理的构造方法

我们考虑带上的循环扩散随机游走。我们提出了有限子域的格林函数的构造条件，这意味着具有多项式误差界限的中心极限定理、局部极限定理和粒子过程所观察到的环境混合。我们的条件可以在广泛的环境中得到验证，包括独立环境、准周期环境和在无穷远处渐近恒定的环境。所提出的条件是针对固定环境的，特别是没有强加平稳条件。