{
  "id": "1911.04159",
  "version": "v1",
  "published": "2019-11-11T10:18:17.000Z",
  "updated": "2019-11-11T10:18:17.000Z",
  "title": "Critical site percolation in high dimension",
  "authors": [
    "Markus Heydenreich",
    "Kilian Matzke"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We use the lace expansion to prove an infra-red bound for site percolation on the hypercubic lattice in high dimension. This implies the triangle condition and allows us to deduce to derive several critical exponents that characterize mean-field behavior in high dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-11T10:18:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "high dimension",
      "critical site percolation",
      "lace expansion",
      "hypercubic lattice",
      "triangle condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}