{
  "id": "1509.01180",
  "version": "v1",
  "published": "2015-09-03T17:48:43.000Z",
  "updated": "2015-09-03T17:48:43.000Z",
  "title": "Decomposition of Brownian loop-soup clusters",
  "authors": [
    "Wei Qian",
    "Wendelin Werner"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the structure of Brownian loop-soup clusters in two dimensions. Among other things, we obtain the following decomposition of the clusters with critical intensity: When one conditions a loop-soup cluster by its outer boundary $\\gamma$ (which is known to be an SLE(4)-type loop), then the union of all excursions away from $\\gamma$ by all the Brownian loops in the loop-soup that touch $\\gamma$ is distributed exactly like the union of all excursions of a Poisson point process of Brownian excursions in the domain enclosed by $\\gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-03T17:48:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brownian loop-soup clusters",
      "decomposition",
      "poisson point process",
      "brownian excursions",
      "excursions away"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150901180Q"
    }
  }
}