Large deviations in random media of zero mean asymmetric zero range processes

We consider an asymmetric zero range process with zero mean in infinite volume with random jump rates starting from equilibrium. We investigate large deviations from hydrodynamical limit of the empirical distribution of particles and prove an upper and lower bound for a large deviation principle. Our main argument is based on a super-exponential estimate in infinite volume. We adapt a method developed by Kipnis \& al. (1989) and Benois \& al. (1995).