Supercriticality conditions for asymmetric zero-range process with sitewise disorder

We discuss necessary and sufficient conditions for the convergence of disordered asymmetric zero-range process to the critical invariant measures.

Supercritical behavior of asymmetric zero-range process with sitewise disorder

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.

Strong hydrodynamic limit for attractive particle systems on Z

We prove almost sure Euler hydrodynamics for a large class of attractive particle systems on $Z$ starting from an arbitrary initial profile. We generalize earlier works by Seppalainen (1999) and Andjel et al. (2004). Our constructive approach requires new ideas since the subadditive ergodic theorem (central to previous works) is no longer effective in our setting.