{
  "id": "math/0310210",
  "version": "v3",
  "published": "2003-10-15T01:13:45.000Z",
  "updated": "2006-02-09T13:45:16.000Z",
  "title": "The harmonic explorer and its convergence to SLE(4)",
  "authors": [
    "Oded Schramm",
    "Scott Sheffield"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117905000000477 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "AnnalsProbab.33:2127-2148,2005",
  "doi": "10.1214/009117905000000477",
  "categories": [
    "math.PR",
    "math-ph",
    "math.CV",
    "math.MP"
  ],
  "abstract": "The harmonic explorer is a random grid path. Very roughly, at each step the harmonic explorer takes a turn to the right with probability equal to the discrete harmonic measure of the left-hand side of the path from a point near the end of the current path. We prove that the harmonic explorer converges to SLE(4) as the grid gets finer.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-02-09T13:45:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "82B43"
    ],
    "keywords": [
      "convergence",
      "random grid path",
      "discrete harmonic measure",
      "harmonic explorer converges",
      "left-hand side"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 640785,
      "adsabs": "2003math.....10210S"
    }
  }
}