{
  "id": "2405.08347",
  "version": "v1",
  "published": "2024-05-14T06:38:08.000Z",
  "updated": "2024-05-14T06:38:08.000Z",
  "title": "Tree walks and the spectrum of random graphs",
  "authors": [
    "Eva-Maria Hainzl",
    "Élie de Panafieu"
  ],
  "comment": "26 pages, long version of a paper presented at the 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)",
  "categories": [
    "math.CO",
    "math.SP"
  ],
  "abstract": "It is a classic result in spectral theory that the limit distribution of the spectral measure of random graphs G(n, p) converges to the semicircle law in case np tends to infinity with n. The spectral measure for random graphs G(n, c/n) however is less understood. In this work, we combine and extend two combinatorial approaches by Bauer and Golinelli (2001) and Enriquez and Menard (2016) and approximate the moments of the spectral measure by counting walks that span trees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-14T06:38:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random graphs",
      "tree walks",
      "spectral measure",
      "case np tends",
      "spectral theory"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}