Random walk on a 2D anisotropic percolation network

We have studied the variance of a random walk on 2D anisotropic random percolation networks. The problem has been worked out by introducing a generalization of the effective medium approximation. A set of coupled non-linear self-consistent equations must be solved to find the effective rates in each direction. Here we have solved a particular 2D model in its dc-limit. Monte Carlo simulations have been made to show the agreement with our theoretical predictions.