{
  "id": "2311.07701",
  "version": "v1",
  "published": "2023-11-13T19:38:46.000Z",
  "updated": "2023-11-13T19:38:46.000Z",
  "title": "The process of fluctuations of the giant component of an Erdős-Rényi graph",
  "authors": [
    "Nathanaël Enriquez",
    "Gabriel Faraud",
    "Sophie Lemaire"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We present a detailed study of the evolution of the giant component of the Erd\\H{o}s-R\\'enyi graph process as the mean degree increases from 1 to infinity. It leads to the identification of the limiting process of the rescaled fluctuations of its order around its deterministic asymptotic. This process is Gaussian with an explicit covariance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-13T19:38:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60F17"
    ],
    "keywords": [
      "giant component",
      "erdős-rényi graph",
      "mean degree increases",
      "explicit covariance",
      "deterministic asymptotic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}