Mathematics – Probability
Scientific paper
2002-01-03
Mathematics
Probability
30 pages version 2: some typos corrected, some remarks added
Scientific paper
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, mysanthropic, `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 \emph{partial extension} of T. Sepp\"al\"ainen's recent paper. 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 Sepp\"al\"ainen's cited paper, but our method does not seem to work for $\beta\ge1/5$.
Toth Balint
Valkó Benedek
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