{
  "id": "1509.06994",
  "version": "v1",
  "published": "2015-09-23T14:09:55.000Z",
  "updated": "2015-09-23T14:09:55.000Z",
  "title": "Stationary random graphs on $\\mathbb{Z}$ with prescribed iid degrees and finite mean connections",
  "authors": [
    "Maria Deijfen",
    "Johan Jonasson"
  ],
  "journal": "Electronic Communications in Probability 11, 336-346 (2006)",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $F$ be a probability distribution with support on the non-negative integers. A model is proposed for generating stationary simple graphs on $\\mathbb{Z}$ with degree distribution $F$ and it is shown for this model that the expected total length of all edges at a given vertex is finite if $F$ has finite second moment. It is not hard to see that any stationary model for generating simple graphs on $\\mathbb{Z}$ will give infinite mean for the total edge length per vertex if $F$ does not have finite second moment. Hence, finite second moment of $F$ is a necessary and sufficient condition for the existence of a model with finite mean total edge length.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-23T14:09:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary random graphs",
      "finite mean connections",
      "prescribed iid degrees",
      "finite second moment",
      "finite mean total edge length"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150906994D"
    }
  }
}