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Mathieu, P.; Piatnitski, A.

Quenched invariance principles for random walks on percolation clusters. (English) Zbl 1131.82012

Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 463, No. 2085, 2287-2307 (2007).
Summary: We consider a supercritical Bernoulli percolation model in \(\mathbb Z^{d}\), \(d\geq 2\), and study the simple symmetric random walk on the infinite percolation cluster. The aim of this paper is to prove the almost sure (quenched) invariance principle for this random walk.

Cited in 87 Documents

MSC:

82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
60F17 Functional limit theorems; invariance principles
60G50 Sums of independent random variables; random walks
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation

Keywords:

percolation; random walk; invariance principle; infinite cluster
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\textit{P. Mathieu} and \textit{A. Piatnitski}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 463, No. 2085, 2287--2307 (2007; Zbl 1131.82012)
Full Text: DOI arXiv

References:

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