The quenched invariance principle for random walks in random   environments admitting a bounded cycle representation
  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. 
Jean-Dominique Deuschel, Holger K\"osters