{
  "id": "math/9911205",
  "version": "v2",
  "published": "1999-11-25T18:02:06.000Z",
  "updated": "2000-03-14T12:43:16.000Z",
  "title": "Convergence to the maximal invariant measure for a zero-range process with random rates",
  "authors": [
    "Enrique D. Andjel",
    "Pablo A. Ferrari",
    "Herve Guiol",
    "Claudio Landim"
  ],
  "comment": "19 pages, Revised version",
  "journal": "Stochastic Processes and their Applications 2000, Vol 90, No. 1, 67--81",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a one-dimensional totally asymmetric nearest-neighbor zero-range process with site-dependent jump-rates - an environment. For each environment p we prove that the set of all invariant measures is the convex hull of a set of product measures with geometric marginals. As a consequence we show that for environments p satisfying certain asymptotic property, there are no invariant measures concentrating on configurations with critical density bigger than $\\rho^*(p)$, a critical value. If $\\rho^*(p)$ is finite we say that there is phase-transition on the density. In this case we prove that if the initial configuration has asymptotic density strictly above $\\rho^*(p)$, then the process converges to the maximal invariant measure.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-03-14T12:43:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22"
    ],
    "keywords": [
      "maximal invariant measure",
      "random rates",
      "one-dimensional totally asymmetric nearest-neighbor zero-range",
      "totally asymmetric nearest-neighbor zero-range process",
      "convergence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....11205A"
    }
  }
}