{
  "id": "2009.07029",
  "version": "v1",
  "published": "2020-09-12T06:23:10.000Z",
  "updated": "2020-09-12T06:23:10.000Z",
  "title": "A Lemma for Color Switching on the Square Lattice",
  "authors": [
    "Philippe Sosoe",
    "Lily Z. Wang"
  ],
  "comment": "10 pages, 2 figures. arXiv admin note: text overlap with arXiv:2001.07872",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider 2d critical Bernoulli percolation on the square lattice. We prove an approximate color-switching lemma comparing k arm probabilities for different polychromatic color sequences. This result is well-known for site percolation on the triangular lattice in [Nolin08]. To handle the complications arising from the dual lattice, we introduce a shifting transformation to convert arms between the primal and the dual lattices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-12T06:23:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B43",
      "60K35"
    ],
    "keywords": [
      "square lattice",
      "color switching",
      "dual lattice",
      "2d critical bernoulli percolation",
      "polychromatic color sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}