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On the Anisotropic Walk on the Supercritical Percolation Cluster

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We investigate in this work the asymptotic behavior of an anisotropic random walk on the supercritical cluster for bond percolation on ℤd, d≥2. 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.

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  1. Departement Mathematik, ETH-Zentrum, 8092, Zürich, Switzerland

    Alain-Sol Sznitman

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  1. Alain-Sol Sznitman
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Communicated by J.L. Lebowitz

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Sznitman, AS. On the Anisotropic Walk on the Supercritical Percolation Cluster. Commun. Math. Phys. 240, 123–148 (2003). https://doi.org/10.1007/s00220-003-0896-3

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