Random walks on weighted, oriented percolation clusters

TL;DR

This paper investigates the conditions under which a weighted random walk on an oriented percolation cluster's backbone converges to Brownian motion, considering complex environmental factors like non-Markovian dynamics and non-ellipticity.

Contribution

It generalizes previous results by establishing necessary weight conditions for Brownian scaling limits in a complex, dynamic random environment.

Findings

Identifies weight conditions for Brownian scaling limits.

Extends previous models to non-elliptic, non-Markovian environments.

Provides a framework for understanding random walks in dynamic percolation clusters.

Abstract

We consider a weighted random walk on the backbone of an oriented percolation cluster. We determine necessary conditions on the weights for Brownian scaling limits under the annealed and the quenched law. This model is a random walk in dynamic random environment (RWDRE), where the environment is mixing, non-Markovian and not elliptic. We provide a generalization of results obtained previously by Birkner et al. (2013).