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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
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