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Quenched invariance principles for walks on clusters of percolation or among random conductances. (English) Zbl 1070.60090
The authors consider two examples of random walks in random environment and prove that, for a.a. realizations of the environment, the process converges in law to a Brownian motion. The first example is a random walk on the infinite cluster of i.i.d. bond percolation on \(\mathbb{Z}^d\), where \(d\geq 4\). The second example is a random walk among i.i.d. random conductances along nearest neighbour edges on \(\mathbb{Z}^d\), for any \(d\geq 1\).

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F05 Central limit and other weak theorems
60F17 Functional limit theorems; invariance principles
60G50 Sums of independent random variables; random walks
82B43 Percolation
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