On the Anisotropic Walk on the Supercritical Percolation Cluster

We investigate in this work the asymptotic behavior of an anisotropic random walk on the supercritical cluster for bond percolation on ^d, d2. 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.