{
  "id": "0805.1326",
  "version": "v2",
  "published": "2008-05-09T11:03:38.000Z",
  "updated": "2009-08-28T02:03:30.000Z",
  "title": "Hydrodynamic limit of particle systems with long jumps",
  "authors": [
    "M. Jara"
  ],
  "comment": "Extended version, uniqueness of hydrodynamic equation and general initial profiles added",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider some interacting particle processes with long-range dynamics: the zero-range and exclusion processes with long jumps. We prove that the hydrodynamic limit of these processes corresponds to a (possibly non-linear) fractional heat equation. The scaling in this case is superdiffusive. In addition, we discuss a central limit theorem for a tagged particle on the zero-range process and existence and uniqueness of solutions of the Cauchy problem for the fractional heat equation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-28T02:03:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "35K55"
    ],
    "keywords": [
      "long jumps",
      "hydrodynamic limit",
      "particle systems",
      "fractional heat equation",
      "central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.1326J"
    }
  }
}