{
  "id": "0711.4070",
  "version": "v1",
  "published": "2007-11-26T18:02:41.000Z",
  "updated": "2007-11-26T18:02:41.000Z",
  "title": "Hausdorff dimension of the SLE curve intersected with the real line",
  "authors": [
    "Tom Alberts",
    "Scott Sheffield"
  ],
  "comment": "24 pages, 9 figures",
  "journal": "Electron. Jour. Probab., 13:1166-1188 (electronic), 2008",
  "categories": [
    "math.PR"
  ],
  "abstract": "We establish an upper bound on the asymptotic probability of an SLE(kappa) curve hitting two small intervals on the real line as the interval width goes to zero, for the range 4 < kappa < 8. As a consequence we are able to prove that the SLE curve intersected with the real line has Hausdorff dimension 2-8/kappa, almost surely.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-26T18:02:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "60K35",
      "28A80"
    ],
    "keywords": [
      "sle curve",
      "real line",
      "hausdorff dimension",
      "interval width",
      "upper bound"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.4070A"
    }
  }
}