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Between Equilibrium Fluctuations and Eulerian Scaling: Perturbation of Equilibrium for a Class of Deposition Models

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Abstract

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 rather than coupling arguments. The result is partial extension of T. Seppäläinen's recent paper. For 0<β<1/5 fixed, we prove that, rescaling microscopic space and time by N, respectively N 1+β, the macroscopic evolution of perturbations of microscopic order N β of the equilibrium states is governed by Burgers' equation. The same statement should hold for 0<β<1/2 as in Seppäläinen's cited paper, but our method does not seem to work for β≥1/5.

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Tóth, B., Valkó, B. Between Equilibrium Fluctuations and Eulerian Scaling: Perturbation of Equilibrium for a Class of Deposition Models. Journal of Statistical Physics 109, 177–205 (2002). https://doi.org/10.1023/A:1019987628197

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