{
  "id": "1609.06626",
  "version": "v1",
  "published": "2016-09-21T16:40:41.000Z",
  "updated": "2016-09-21T16:40:41.000Z",
  "title": "Arm events in two-dimensional invasion percolation",
  "authors": [
    "Michael Damron",
    "Jack Hanson",
    "Philippe Sosoe"
  ],
  "comment": "37 pages, 9 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We compare the probabilities of arm events in two-dimensional invasion percolation to those in critical percolation. Arm events are defined by the existence of a prescribed color sequence of invaded and non-invaded connections from the origin to distance n. We find that, for sequences of a particular form, arm probabilities in invasion percolation and critical percolation are comparable, uniformly in n, while they differ by a power of n for all others. A corollary of our results is the existence, on the triangular lattice, of arm exponents for invasion percolation, for any color sequence with at least two open (invaded) entries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-21T16:40:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "two-dimensional invasion percolation",
      "arm events",
      "critical percolation",
      "prescribed color sequence",
      "arm probabilities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}