{
  "id": "math/0201030",
  "version": "v1",
  "published": "2002-01-04T18:56:21.000Z",
  "updated": "2002-01-04T18:56:21.000Z",
  "title": "The lowest crossing in 2D critical percolation",
  "authors": [
    "J. van den Berg",
    "A. A. Jarai"
  ],
  "comment": "16 pages, Latex, 2 eps figures, special macros: percmac.tex. Submitted to Annals of Probability",
  "journal": "Ann. Probab. 31 (2003), no. 3, 1241-1253",
  "doi": "10.1214/aop/1055425778",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the following problem for critical site percolation on the triangular lattice. Let A and B be sites on a horizontal line e separated by distance n. Consider, in the half-plane above e, the lowest occupied crossing R from the half-line left of A to the half-line right of B. We show that the probability that R has a site at distance smaller than m from AB is of order (log (n/m))^{-1}, uniformly in 1 <= m < n/2. Much of our analysis can be carried out for other two-dimensional lattices as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-01-04T18:56:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "2d critical percolation",
      "lowest crossing",
      "half-line right",
      "half-line left",
      "critical site percolation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1030V"
    }
  }
}