{
  "id": "cond-mat/0512622",
  "version": "v1",
  "published": "2005-12-23T18:27:47.000Z",
  "updated": "2005-12-23T18:27:47.000Z",
  "title": "One-Dimensional Directed Sandpile Models and the Area under a Brownian Curve",
  "authors": [
    "M A Stapleton",
    "K Christensen"
  ],
  "comment": "24 pages, 5 figures",
  "doi": "10.1088/0305-4470/39/29/007",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We derive the steady state properties of a general directed ``sandpile'' model in one dimension. Using a central limit theorem for dependent random variables we find the precise conditions for the model to belong to the universality class of the Totally Asymmetric Oslo model, thereby identifying a large universality class of directed sandpiles. We map the avalanche size to the area under a Brownian curve with an absorbing boundary at the origin, motivating us to solve this Brownian curve problem. Thus, we are able to determine the moment generating function for the avalanche-size probability in this universality class, explicitly calculating amplitudes of the leading order terms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-23T18:27:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "one-dimensional directed sandpile models",
      "dependent random variables",
      "central limit theorem",
      "steady state properties",
      "totally asymmetric oslo model"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2006,
      "month": "Jul",
      "volume": 39,
      "number": 29,
      "pages": 9107
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006JPhA...39.9107S"
    }
  }
}