{
  "id": "1507.04786",
  "version": "v1",
  "published": "2015-07-16T22:32:56.000Z",
  "updated": "2015-07-16T22:32:56.000Z",
  "title": "Equilibrium Fluctuations for a Discrete Atlas Model",
  "authors": [
    "F. Hernández",
    "M. Jara",
    "Fabio J. Valentim"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider a discrete version of the Atlas model, which corresponds to a sequence of zero-range processes on a semi-infinite line, with a source at the origin and a diverging density of particles. We show that the equilibrium fluctuations of this model are governed by a stochastic heat equation with Neumann boundary conditions. As a consequence, we show that the current of particles at the origin converges to a fractional Brownian motion of Hurst exponent H=1/4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-16T22:32:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60H15",
      "82C22"
    ],
    "keywords": [
      "discrete atlas model",
      "equilibrium fluctuations",
      "stochastic heat equation",
      "neumann boundary conditions",
      "fractional brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150704786H"
    }
  }
}