{
  "id": "math/0605266",
  "version": "v3",
  "published": "2006-05-10T15:02:14.000Z",
  "updated": "2006-10-23T17:46:55.000Z",
  "title": "$t^{1/3}$ Superdiffusivity of Finite-Range Asymmetric Exclusion Processes on $\\mathbb Z$",
  "authors": [
    "Jeremy Quastel",
    "Benedek Valko"
  ],
  "comment": "Version 3. Statement of Theorem 3 is corrected",
  "doi": "10.1007/s00220-007-0242-2",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider finite-range asymmetric exclusion processes on $\\mathbb Z$ with non-zero drift. The diffusivity $D(t)$ is expected to be of ${\\mathcal O}(t^{1/3})$. We prove that $D(t)\\ge Ct^{1/3}$ in the weak (Tauberian) sense that $\\int_0^\\infty e^{-\\lambda t}tD(t)dt \\ge C\\lambda^{-7/3}$ as $\\lambda\\to 0$. The proof employs the resolvent method to make a direct comparison with the totally asymmetric simple exclusion process, for which the result is a consequence of the scaling limit for the two-point function recently obtained by Ferrari and Spohn. In the nearest neighbor case, we show further that $tD(t)$ is monotone, and hence we can conclude that $D(t)\\ge Ct^{1/3}(\\log t)^{-7/3}$ in the usual sense.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-10-23T17:46:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22"
    ],
    "keywords": [
      "finite-range asymmetric exclusion processes",
      "totally asymmetric simple exclusion process",
      "superdiffusivity",
      "nearest neighbor case",
      "usual sense"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}