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Between equilibrium fluctuations and Eulerian scaling: Perturbation of equilibrium for a class of deposition models. (English) Zbl 1027.82031
Summary: We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, $$K$$-exclusion, misanthropic, “bricklayers” models, and much more. We do not assume attractivity of the interactions. We apply Yau’s relative entropy method [H. T. Yau, Lett. Math. Phys. 22, 63-80 (1991; Zbl 0725.60120)] rather than coupling arguments. The result is a partial extension of T. Seppäläinen’s recent paper [Ann. Probab. 29, 176-204 (2001; Zbl 1014.60091)]. For $$0<\beta<1/5$$ fixed, we prove that, rescaling microscopic space and time by $$N$$, respectively $$N^{1+\beta}$$, the macroscopic evolution of perturbations of microscopic order $$N^{-\beta}$$ of the equilibrium states is governed by Burgers’ equation. The same statement should hold for $$0<\beta<1/2$$ as in Seppäläinen’s cited paper, but our method does not seem to work for $$\beta\geqslant 1/5$$.

##### MSC:
 82C22 Interacting particle systems in time-dependent statistical mechanics 60K35 Interacting random processes; statistical mechanics type models; percolation theory
##### Keywords:
Hydrodynamic limit; relative entropy; Burgers’ equation
##### Citations:
Zbl 0725.60120; Zbl 1014.60091
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