The quenched invariance principle for random walks in random environments admitting a bounded cycle representation

TL;DR

This paper establishes a quenched invariance principle for random walks in environments with transition probabilities based on bounded cycles, extending previous work to non-reversible settings.

Contribution

It introduces a novel approach to prove the invariance principle for non-reversible random walks using bounded cycle representations.

Findings

Proves a quenched invariance principle for a new class of random walks.

Extends techniques from reversible to non-reversible environments.

Adapts existing proofs to broader settings.

Abstract

We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random conductances by Sidoravicius and Sznitman (Probab. Theory Related Fields 129 (2004) 219--244) to the non-reversible setting.