Hydrodynamic behavior of symmetric zero-range processes with random rates

We consider a nearest-neighbor symmetric zero-range process, evolving on the d-dimensional periodic lattice, with a random jump rate and investigate its hydrodynamic behavior. We prove that the empirical distribution of particles converges in probability to the weak solution of the non-linear diffusion equation. Our approach follows the method of entropy production introduced by Guo et al. (1988, Comm. Math. Phys. 118, 31-59). We adapt and generalize some results in Benjamini et al. (1996, Stochastic Process. Appl. 61, 181-204).