A conditional quenched CLT for random walks among random conductances on $\mathbb{Z}^d$

Christophe Gallesco, Nina Gantert, Serguei Popov, Marina Vachkovskaia

Published 2011-08-29, updated 2013-03-09Version 2

Consider a random walk among random conductances on $\mathbb{Z}^d$ with $d\geq 2$. We study the quenched limit law under the usual diffusive scaling of the random walk conditioned to have its first coordinate positive. We show that the conditional limit law is the product of a Brownian meander and a $(d-1)$-dimensional Brownian motion.