{
  "id": "2108.08116",
  "version": "v1",
  "published": "2021-08-18T12:37:41.000Z",
  "updated": "2021-08-18T12:37:41.000Z",
  "title": "$γ$-variable first-order logic of preferential attachment random graphs",
  "authors": [
    "Yury Malyshkin"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study logical limit laws for preferential attachment random graphs. In this random graph model, vertices and edges are introduced recursively: at time $1$, we start with vertices $0,1$ and $m$ edges between them. At step $n+1$ the vertex $n+1$ is introduced together with $m$ edges joining the new vertex with $m$ vertices chosen from $1,\\ldots,n$ independently with probabilities proportional to their degrees plus a positive parameter $\\delta$. We prove that this random graph obeys the convergence law for first-order sentences with at most $m-2$ variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-18T12:37:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80"
    ],
    "keywords": [
      "preferential attachment random graphs",
      "variable first-order logic",
      "random graph model",
      "study logical limit laws",
      "random graph obeys"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}