{
  "id": "1509.07026",
  "version": "v1",
  "published": "2015-09-23T15:18:31.000Z",
  "updated": "2015-09-23T15:18:31.000Z",
  "title": "Stationary random graphs with prescribed iid degrees on a spatial Poisson process",
  "authors": [
    "Maria Deijfen"
  ],
  "journal": "Electronic Communications in Probability 14, 81-89 (2009)",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $[\\mathcal{P}]$ be the points of a Poisson process on $\\mathbb{R}^d$ and $F$ a probability distribution with support on the non-negative integers. Models are formulated for generating translation invariant random graphs with vertex set $[\\mathcal{P}]$ and iid vertex degrees with distribution $F$, and the length of the edges is analyzed. The main result is that finite mean for the total edge length per vertex is possible if and only if $F$ has finite moment of order $(d+1)/d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-23T15:18:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary random graphs",
      "spatial poisson process",
      "prescribed iid degrees",
      "generating translation invariant random graphs",
      "iid vertex degrees"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150907026D"
    }
  }
}