{
  "id": "1905.12326",
  "version": "v1",
  "published": "2019-05-29T11:04:41.000Z",
  "updated": "2019-05-29T11:04:41.000Z",
  "title": "Fluctuations of the Magnetization for Ising Models on Dense Erdős-Rényi Random Graphs",
  "authors": [
    "Zakhar Kabluchko",
    "Matthias Löwe",
    "Kristina Schubert"
  ],
  "comment": "19 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We analyze Ising/Curie-Weiss models on the (directed) Erd\\H{o}s-R\\'enyi random graph on $N$ vertices in which every edge is present with probability $p$. These models were introduced by Bovier and Gayrard [J. Stat. Phys., 1993]. We prove a quenched Central Limit Theorem for the magnetization in the high-temperature regime $\\beta<1$ when $p=p(N)$ satisfies $p^3N^2\\to +\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-29T11:04:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dense erdős-rényi random graphs",
      "ising models",
      "magnetization",
      "fluctuations",
      "analyze ising/curie-weiss models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}