On the Anisotropic Walk on the Supercritical Percolation Cluster |
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Authors: | Alain-Sol Sznitman |
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Institution: | (1) Departement Mathematik, ETH-Zentrum, 8092 Zürich,, Switzerland |
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Abstract: | We investigate in this work the asymptotic behavior of an anisotropic random walk on the supercritical cluster for bond percolation on d, 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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