A conditional quenched CLT for random walks among random conductances on \({\mathbb Z}^d\). (English) Zbl 1311.60049
Summary: 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 a linear transformation of the product law of a Brownian meander and a \((d-1)\)-dimensional Brownian motion.
MSC:
60G50 | Sums of independent random variables; random walks |
60J65 | Brownian motion |
60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
60K37 | Processes in random environments |