Quenched invariance principle for random walk in time-dependent balanced random environment

TL;DR

This paper establishes a quenched invariance principle for balanced random walks in time-dependent ergodic environments, extending previous results to non-nearest neighbor cases using a maximum principle approach.

Contribution

It proves a quenched central limit theorem for a broad class of time-dependent, balanced, ergodic random environments, including non-nearest neighbor walks.

Findings

Proves a quenched invariance principle for such random walks.

Extends results to non-nearest neighbor environments.

Uses maximum principle for parabolic difference operators.

Abstract

We prove a quenched central limit theorem for balanced random walks in time dependent ergodic random environments which is not necessarily nearest-neigbhor. We assume that the environment satisfies appropriate ergodicity and ellipticity conditions. The proof is based on the use of a maximum principle for parabolic difference operators.