Hydrodynamic limit for attractive particle systems on \(\mathbb{Z}{}^ d\). (English) Zbl 0738.60098

Rezakhanlou, Fraydoun

Commun. Math. Phys. 140, No. 3, 417-448 (1991).

Summary: We study the hydrodynamic behavior of asymmetric simple exclusions and zero range processes in several dimensions. Under Euler scaling, a nonlinear conservation law is derived for the time evolution of the macroscopic particle density.

MSC:

60K35

Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

stochastic particle systems; Markovian law; hydrodynamic behavior; asymmetric simple exclusions; zero range processes; Euler scaling; nonlinear conservation law; time evolution; macroscopic particle density

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