A Conditional Quenched CLT for Random Walks Among Random Conductances on $Z^d$

C. Gallesco, N. Gantert, S.Yu. Popov, M. Vachkovskaia

2014, v.20, Issue 2, 287-328


Consider a random walk among random conductances on $Z^d$ 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 a linear transformation of the product law of a Brownian meander and a $(d-1)$-dimensional Brownian motion.

Keywords: random conductance model,uniform heat kernel bounds,Brownian meander,reversibility


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