{
  "id": "1211.4146",
  "version": "v2",
  "published": "2012-11-17T18:49:02.000Z",
  "updated": "2015-06-19T07:56:40.000Z",
  "title": "Minkowski content and natural parameterization for the Schramm-Loewner evolution",
  "authors": [
    "Gregory F. Lawler",
    "Mohammad A. Rezaei"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/13-AOP874 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2015, Vol. 43, No. 3, 1082-1120",
  "doi": "10.1214/13-AOP874",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove the existence and nontriviality of the $d$-dimensional 4 Minkowski content for the Schramm-Loewner evolution ($\\mathrm {SLE}_{\\kappa}$) with $\\kappa<8$ and $d=1+\\frac{\\kappa}{8}$. We show that this is a multiple of the natural parameterization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-17T18:49:02.000Z",
      "abstract": "We prove that the existence and nontriviality of the d-dimensional Minkowski con- tent for the Schramm-Loewner evolution (SLE{\\kappa}) with ? k<8 and d = 1 + {\\kappa}/8. We show that this is a multiple of the natural paramterization.",
      "comment": "36 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-06-19T07:56:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schramm-loewner evolution",
      "minkowski content",
      "natural parameterization",
      "d-dimensional minkowski"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.4146L"
    }
  }
}