{
  "id": "2305.04716",
  "version": "v1",
  "published": "2023-05-08T14:02:06.000Z",
  "updated": "2023-05-08T14:02:06.000Z",
  "title": "A dynamical approach to spanning and surplus edges of random graphs",
  "authors": [
    "Josué Corujo",
    "Vlada Limic"
  ],
  "comment": "28 pages, 9 figures, improved and upgraded version of arXiv:1703.02574",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Consider a finite inhomogeneous random graph running in continuous time, where each vertex has a mass, and the edge that links any pair of vertices appears with a rate equal to the product of their masses. The simultaneous breadth-first-walk introduced by Limic (2019) is extended in order to account for the surplus edge data in addition to the spanning edge data. Two different graph-based representations of the multiplicative coalescent, with different advantages and drawbacks, are discussed in detail. A canonical multi-graph from Bhamidi, Budhiraja and Wang (2014) naturally emerges. The presented framework will facilitate the understanding of scaling limits with surplus edges for near-critical random graphs in the domain of attraction of general (not necessarily standard) eternal augmented multiplicative coalescent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-08T14:02:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60J90",
      "60C05"
    ],
    "keywords": [
      "dynamical approach",
      "multiplicative coalescent",
      "surplus edge data",
      "vertices appears",
      "rate equal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}