{
  "id": "1302.5436",
  "version": "v3",
  "published": "2013-02-21T21:16:51.000Z",
  "updated": "2013-12-17T21:13:31.000Z",
  "title": "Bond percolation on a non-p.c.f. Sierpiński Gasket, iterated barycentric subdivision of a triangle, and Hexacarpet",
  "authors": [
    "Derek Lougee",
    "Benjamin Steinhurst"
  ],
  "comment": "v3: more revisions in exposition, v2: revised the exposition, 18 pages; v1: 17 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate bond percolation on the iterated barycentric subdivision of a triangle, the hexacarpet, and the non-p.c.f. Sierpinski gasket. With the use of the diamond fractal, we are able to bound the critical probability of percolation on the non-p.c.f. gasket and the iterated barycentric subdivision of a triangle from above by 0.282. We then show how both the gasket and hexacarpet fractals are related via the iterated barycentric subdivisions of a triangle: the two spaces exhibit duality properties although they are not themselves dual graphs. Finally we show the existence of a non-trivial phase transition on all three graphs.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-12-17T21:13:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "28A80",
      "52M20"
    ],
    "keywords": [
      "iterated barycentric subdivision",
      "bond percolation",
      "sierpiński gasket",
      "non-trivial phase transition",
      "sierpinski gasket"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.5436L"
    }
  }
}