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).