{
  "id": "2305.12368",
  "version": "v1",
  "published": "2023-05-21T06:36:25.000Z",
  "updated": "2023-05-21T06:36:25.000Z",
  "title": "A generalization of Cardy's and Schramm's formulae",
  "authors": [
    "Mikhail Khristoforov",
    "Mikhail Skopenkov",
    "Stanislav Smirnov"
  ],
  "comment": "14 pages, 6 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.CV",
    "math.MP"
  ],
  "abstract": "We study critical site percolation on the triangular lattice. We find the difference of the probabilities of having a percolation interface to the right and to the left of two given points in the scaling limit. This generalizes both Cardy's and Schramm's formulae. The generalization involves a new interesting discrete analytic observable and an unexpected conformal mapping.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-21T06:36:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "30C30",
      "33C05",
      "81T40",
      "82B43"
    ],
    "keywords": [
      "schramms formulae",
      "generalization",
      "study critical site percolation",
      "triangular lattice",
      "percolation interface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}