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Zbl 1087.82011
Sznitman, Alain-Sol
On the anisotropic walk on the supercritical percolation cluster. (English)
[J] Commun. Math. Phys. 240, No. 1-2, 123-148 (2003). ISSN 0010-3616; ISSN 1432-0916/e

Summary: We investigate in this work the asymptotic behavior of an anisotropic random walk on the supercritical cluster for bond percolation on $\Bbb Z^d$, $d\ge2$. In particular we show that for small anisotropy the walk behaves in a ballistic fashion, whereas for strong anisotropy the walk is sub-diffusive. For arbitrary anisotropy, we also prove the directional transience of the walk and construct a renewal structure.

MSC 2000:: *82B43 Percolation
60K35 Interacting random processes
60G50 Sums of independent random variables
82B41 Random walks, etc. (statistical mechanics)

Cited in: Zbl 1196.60159

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