{
  "id": "math/0201016",
  "version": "v2",
  "published": "2002-01-03T09:41:18.000Z",
  "updated": "2002-01-07T15:36:41.000Z",
  "title": "Between equilibrium fluctuations and Eulerian scaling: Perturbation of equilibrium for a class of deposition models",
  "authors": [
    "Balint Toth",
    "Benedek Valko"
  ],
  "comment": "30 pages version 2: some typos corrected, some remarks added",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "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, 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 $\\beta\\ge1/5$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-01-07T15:36:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deposition models",
      "equilibrium fluctuations",
      "perturbation",
      "eulerian scaling",
      "equilibrium states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1016T"
    }
  }
}