A quenched invariance principle for certain ballistic random walks in i.i.d. environments

Abstract

We prove that every random walk in i.i.d. environment in dimension greater than or equal to 2 that has an almost sure positive speed in a certain direction, an annealed invariance principle and some mild integrability condition for regeneration times also satisfies a quenched invariance principle. The argument is based on intersection estimates and a theorem of Bolthausen and Sznitman.

This version includes an extension of the results to cover also dimensions 2,3, and also corrects several minor innacuracies. The previous version included a correction of a minor error in (3.21) (used for d=4); The correction pushed the assumption on moments of regeneration times to >8