{
  "id": "math/0011008",
  "version": "v5",
  "published": "2000-11-01T18:21:28.000Z",
  "updated": "2003-01-18T16:19:57.000Z",
  "title": "Compatible sequences and a slow Winkler percolation",
  "authors": [
    "Peter Gacs"
  ],
  "comment": "33 pages, 8 figures. Submitted to Combinatorics, Probability and Computing. Some errors corrected",
  "journal": "Combinatorics, Probability and Computing 13 (2004) pp. 815-856",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Two infinite 0-1 sequences are called compatible when it is possible to cast out 0's from both in such a way that they become complementary to each other. Answering a question of Peter Winkler, we show that if the two 0-1-sequences are random i.i.d. and independent from each other, with probability p of 1's, then if p is sufficiently small they are compatible with positive probability. The question is equivalent to a certain dependent percolation with a power-law behavior: the probability that the origin is blocked at distance n but not closer decreases only polynomially fast and not, as usual, exponentially.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2003-01-18T16:19:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B43",
      "60K35"
    ],
    "keywords": [
      "slow winkler percolation",
      "compatible sequences",
      "peter winkler",
      "dependent percolation",
      "power-law behavior"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....11008G"
    }
  }
}