{
  "id": "2405.10756",
  "version": "v1",
  "published": "2024-05-17T13:08:36.000Z",
  "updated": "2024-05-17T13:08:36.000Z",
  "title": "Hitting times in the binomial random graph",
  "authors": [
    "Bertille Granet",
    "Felix Joos",
    "Jonathan Schrodt"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "Fix $k\\geq 2$, choose $\\frac{\\log n}{n^{(k-1)/k}}\\leq p\\leq 1-\\Omega(\\frac{\\log^4 n}{n})$, and consider $G\\sim G(n,p)$. For any pair of vertices $v,w\\in V(G)$, we give a simple and precise formula for the expected number of steps that a random walk on $G$ starting at $w$ needs to first arrive at $v$. The formula only depends on basic structural properties of $G$. This improves and extends recent results of Ottolini and Steinerberger, as well as Ottolini, who considered this problem for constant as well as for mildly vanishing $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-17T13:08:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "binomial random graph",
      "hitting times",
      "basic structural properties",
      "precise formula",
      "random walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}