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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