{
  "id": "1910.05820",
  "version": "v1",
  "published": "2019-10-13T19:48:30.000Z",
  "updated": "2019-10-13T19:48:30.000Z",
  "title": "Resolution of a conjecture on majority dynamics: rapid stabilisation in dense random graphs",
  "authors": [
    "Nikolaos Fountoulakis",
    "Mihyun Kang",
    "Tamás Makai"
  ],
  "comment": "20 pages",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We study majority dynamics on the binomial random graph $G(n,p)$ with $p = d/n$ and $d > \\lambda n^{1/2}$, for some large $\\lambda>0$. In this process, each vertex has a state in $\\{-1,+1 \\}$ and at each round every vertex adopts the state of the majority of its neighbours, retaining its state in the case of a tie. We show that with high probability the process reaches unanimity in at most four rounds. This confirms a conjecture of Benjamini, Chan, O' Donnel, Tamuz and Tan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-13T19:48:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80"
    ],
    "keywords": [
      "dense random graphs",
      "rapid stabilisation",
      "conjecture",
      "resolution",
      "binomial random graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}