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We establish necessary and sufficient conditions for weak convergence to the upper invariant measure for asymmetric nearest neighbour zero range processes with non homogeneous jump rates. The class of environments considered is close to that considered by Andjel, Ferrari, Guiol and Landim, while our class of processes is broader. We also give a simpler proof of a result of Ferrari and Sisko with weaker assumptions.
We discuss necessary and sufficient conditions for the convergence of disordered asymmetric zero-range process to the critical invariant measures.
We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. For any given environment satisfying suitable aver
We survey our recent articles dealing with one dimensional attractive zero range processes moving under site disorder. We suppose that the underlying random walks are biased to the right and so hyperbolic scaling is expected. Under the conditions of
We investigate the macroscopic behavior of asymmetric attractive zero-range processes on $mathbb{Z}$ where particles are destroyed at the origin at a rate of order $N^beta$, where $beta in mathbb{R}$ and $Ninmathbb{N}$ is the scaling parameter. We pr
We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites and is un