Totally asymmetric attractive particle systems on \(\mathbb{Z}\): Hydrodynamic limit for general initial profiles (Q1332315)

The hydrodynamic limit of particle systems is an active research topic in the field. It is often quite difficult especially in the asymmetric situations. This paper extends the previous results on the preservation of local equilibrium for two classes of one-dimensional totally asymmetric attractive particle systems: the simple exclusion process and the zero range process. The hydrodynamic behavior is studied for general initial profiles when particles are jumping only to the nearest neighbor in a given direction. The main tool used is the couplings.