Random Walks on Percolation Clusters
Random structures have an intricate relationship with the random walks defined on them. Here we focus on random walks on percolation clusters as a prime example of the random conductance model with the additional charm of not being elliptic. We discuss random walks on supercritical percolation clusters, on finite critical clusters, and on the incipient infinite cluster. The results show that random walks on supercritical and critical percolation structures behave completely differently, underlining the remarkable features of critical structures.