Large deviations for simple random walk on supercritical percolation clusters

Abstract

We prove quenched large deviation principles governing the position of the random walk on a supercritical site percolation on the integer lattice. A feature of this model is non-ellipticity of transition probabilities. Our analysis is based on the consideration of so-called Lyapunov exponents for the Laplace transform of the first passage time. The rate function is given by the Legendre transform of the Lyapunov exponents.