Abstract
We prove conservation of local equilibrium for attractive particle systems. Our method applies as well to gradient asymmetric processes with mean drift 0 under diffusive $(N^2)$ rescaling. The hydrodynamical behavior is proved for bounded continuous initial profiles under Euler $(N)$ rescaling and for bounded a.s. continuous profiles under diffusive rescaling. We prove that, for attractive systems, the conservation of local equilibrium follows from a law of large numbers for the density field.
Citation
C. Landim. "Conservation of Local Equilibrium for Attractive Particle Systems on $Z^d$." Ann. Probab. 21 (4) 1782 - 1808, October, 1993. https://doi.org/10.1214/aop/1176989000
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