{
  "id": "1309.0269",
  "version": "v3",
  "published": "2013-09-01T21:54:13.000Z",
  "updated": "2017-01-25T21:07:42.000Z",
  "title": "The scaling limits of the Minimal Spanning Tree and Invasion Percolation in the plane",
  "authors": [
    "Christophe Garban",
    "Gábor Pete",
    "Oded Schramm"
  ],
  "comment": "56 pages, 21 figures. A thoroughly revised version",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that the Minimal Spanning Tree and the Invasion Percolation Tree on a version of the triangular lattice in the complex plane have unique scaling limits, which are invariant under rotations, scalings, and, in the case of the MST, also under translations. However, they are not expected to be conformally invariant. We also prove some geometric properties of the limiting MST. The topology of convergence is the space of spanning trees introduced by Aizenman, Burchard, Newman & Wilson (1999), and the proof relies on the existence and conformal covariance of the scaling limit of the near-critical percolation ensemble, established in our earlier works.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-13T20:55:32.000Z",
      "comment": "50 pages, 18 figures. In this version, small changes throughout, and some added references",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2017-01-25T21:07:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimal spanning tree",
      "invasion percolation tree",
      "unique scaling limits",
      "geometric properties",
      "proof relies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.0269G"
    }
  }
}