Constructive approach to limit theorems for recurrent diffusive random walks on a strip
Probability
2020-08-26 v1
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.
Cite
@article{arxiv.2008.11072,
title = {Constructive approach to limit theorems for recurrent diffusive random walks on a strip},
author = {Dmitry Dolgopyat and Ilya Goldsheid},
journal= {arXiv preprint arXiv:2008.11072},
year = {2020}
}