{
  "id": "1910.12715",
  "version": "v1",
  "published": "2019-10-28T14:36:11.000Z",
  "updated": "2019-10-28T14:36:11.000Z",
  "title": "Dynamical Models for Random Simplicial Complexes",
  "authors": [
    "Nikolaos Fountoulakis",
    "Tejas Iyer",
    "Cécile Mailler",
    "Henning Sulzbach"
  ],
  "comment": "45 pages (main body 37 pages), 4 figures",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We study a general model of random dynamical simplicial complexes and derive a formula for the asymptotic degree distribution. This asymptotic formula encompasses results for a number of existing models, including random Apollonian networks and the weighted random recursive tree. It also confirms results on the scale-free nature of Complex Quantum Network Manifolds in dimensions $d > 2$, and special types of Network Geometry with Flavour models studied in the physics literature by Bianconi, Rahmede [\\textit{Sci. Rep.} \\textbf{5}, 13979 (2015) and \\textit{Phys. Rev. E} \\textbf{93}, 032315 (2016)].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-28T14:36:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90B15",
      "60J20",
      "05C80"
    ],
    "keywords": [
      "random simplicial complexes",
      "dynamical models",
      "asymptotic formula encompasses results",
      "complex quantum network manifolds",
      "random dynamical simplicial complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}