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