{
  "id": "2002.11372",
  "version": "v1",
  "published": "2020-02-26T09:24:46.000Z",
  "updated": "2020-02-26T09:24:46.000Z",
  "title": "Fluctuations for the partition function of Ising models on Erdös-Rényi random graphs",
  "authors": [
    "Zakhar Kabluchko",
    "Matthias Löwe",
    "Kristina Schubert"
  ],
  "comment": "32 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We analyze Ising/Curie-Weiss models on the Erd\\H{o}s-R\\'enyi graph with $N$ vertices and edge probability $p=p(N)$ that were introduced by Bovier and Gayrard [J.\\ Statist.\\ Phys., 72(3-4):643--664, 1993] and investigated in two previous articles by the authors. We prove Central Limit Theorems for the partition function of the model and -- at other decay regimes of $p(N)$ -- for the logarithmic partition function. We find critical regimes for $p(N)$ at which the behavior of the fluctuations of the partition function changes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-26T09:24:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "82B44",
      "82B20"
    ],
    "keywords": [
      "erdös-rényi random graphs",
      "ising models",
      "fluctuations",
      "analyze ising/curie-weiss models",
      "central limit theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}