{
  "id": "1506.08881",
  "version": "v1",
  "published": "2015-06-29T22:12:33.000Z",
  "updated": "2015-06-29T22:12:33.000Z",
  "title": "Sandpiles and unicycles on random planar maps",
  "authors": [
    "Xin Sun",
    "David B. Wilson"
  ],
  "comment": "15 pages. arXiv admin note: text overlap with arXiv:1108.2241 by other authors",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the abelian sandpile model and the uniform spanning unicycle on random planar maps. We show that the sandpile density converges to 5/2 as the maps get large. For the spanning unicycle, we show that the length and area of the cycle converges to the hitting time and location of a simple random walk in the first quadrant. The calculations use the \"hamburger-cheeseburger\" construction of Fortuin--Kasteleyn random cluster configurations on random planar maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-29T22:12:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20",
      "60C05",
      "05C05"
    ],
    "keywords": [
      "random planar maps",
      "fortuin-kasteleyn random cluster configurations",
      "simple random walk",
      "cycle converges",
      "sandpile density converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150608881S"
    }
  }
}