We prove a level-2 quenched large deviation principle for a simple random walk on a supercritical percolation cluster (SRWPC) on the integer lattices. The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long-range correlations, specifically, the random cluster model, the random interlacement and its vacant set, and the level sets of the Gaussian free field. We take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC.
This talk is based on a joint work with Noam Berger and Chiranjib Mukherjee.