{
  "id": "1504.06549",
  "version": "v1",
  "published": "2015-04-24T16:03:15.000Z",
  "updated": "2015-04-24T16:03:15.000Z",
  "title": "A remark on monotonicity in Bernoulli bond Percolation",
  "authors": [
    "Bernardo N. B. de Lima",
    "Aldo Procacci",
    "Rémy Sanchis"
  ],
  "comment": "6 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider an anisotropic independent bond percolation model on the $d$-dimensional hypercubic lattice, $d\\geq 2$, with parameter $p$. We show that the two point connectivity function $P_{p}(\\{(0,\\dots,0)\\leftrightarrow (n,0,\\dots,0)\\})$ is a monotone function in $n$ when the parameter $p$ is close enough to 0. Analogously, we show that truncated connectivity function $P_{p}(\\{(0,\\dots,0)\\leftrightarrow (n,0,\\dots,0), (0,\\dots,0)\\nleftrightarrow\\infty\\})$ is also a monotone function in $n$ when $p$ is close to 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-24T16:03:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20",
      "82B41",
      "82B43"
    ],
    "keywords": [
      "bernoulli bond percolation",
      "anisotropic independent bond percolation model",
      "monotonicity",
      "monotone function",
      "dimensional hypercubic lattice"
    ],
    "publication": {
      "doi": "10.1007/s10955-015-1284-z",
      "journal": "Journal of Statistical Physics",
      "year": 2015,
      "month": "Sep",
      "volume": 160,
      "number": 5,
      "pages": 1244
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JSP...160.1244D"
    }
  }
}