{
  "id": "2410.03647",
  "version": "v1",
  "published": "2024-10-04T17:52:59.000Z",
  "updated": "2024-10-04T17:52:59.000Z",
  "title": "An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d>6$",
  "authors": [
    "Hugo Duminil-Copin",
    "Romain Panis"
  ],
  "comment": "30 pages, 5 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions $d>6$. We obtain an upper bound for the full-space and half-space two-point functions in the critical and near-critical regimes. In a companion paper, we apply a similar analysis to the study of the weakly self-avoiding walk model in dimensions $d>4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-04T17:52:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B27",
      "82B41",
      "60K35",
      "82B27",
      "82B41",
      "82B43"
    ],
    "keywords": [
      "mean-field behaviour",
      "alternative approach",
      "dimensions",
      "sufficiently spread-out bernoulli percolation",
      "half-space two-point functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}