Large deviations for simple random walk on supercritical percolation clusters (Q1932487)

Large deviation principles for simple random walks on a supercritical site percolation have already been dealt with in the literature, mainly with elliptic transition probabilities. The author of this paper goes a step further and states similar results for non-elliptic transition probabilities which originate from the fluctuation of site percolation clusters. The proof is based mainly on the use of the Lyapunov exponent. An upper bound and a lower bound for the large deviations are obtained.