{
  "id": "1409.6834",
  "version": "v1",
  "published": "2014-09-24T05:41:20.000Z",
  "updated": "2014-09-24T05:41:20.000Z",
  "title": "Exploration processes and SLE$_6$",
  "authors": [
    "Jianping Jiang"
  ],
  "comment": "14 pages, 6 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We define radial exploration processes from $a$ to $b$ and from $b$ to $a$ in a domain $D$ of hexagons where $a$ is a boundary point and $b$ is an interior point. We prove the reversibility: the time-reversal of the process from $b$ to $a$ has the same distribution as the process from $a$ to $b$. We show the scaling limit of such an exploration process is a radial SLE$_6$ in $D$. As a consequence, the distribution of the last hitting point with the boundary of any radial SLE$_6$ is the harmonic measure. We also prove the scaling limit of a similar exploration process defined in the full complex plane $\\mathbb{C}$ is the full-plane SLE$_6$. A by-product of these results is that the time-reversal of a radial SLE$_6$ trace after the last visit to the boundary is a full-plane SLE$_6$ trace up to some stopping time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-24T05:41:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43",
      "60J67"
    ],
    "keywords": [
      "radial sle",
      "full-plane sle",
      "define radial exploration processes",
      "scaling limit",
      "similar exploration process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.6834J"
    }
  }
}