{
  "id": "0909.5325",
  "version": "v5",
  "published": "2009-09-29T12:32:58.000Z",
  "updated": "2014-04-15T17:49:57.000Z",
  "title": "Percolation for the stable marriage of Poisson and Lebesgue with random appetites",
  "authors": [
    "Daniel Andrés D\\'\\iaz Pachón"
  ],
  "comment": "12 pages. Final version",
  "journal": "Stochastics, Vol. 85, Issue 2, pp. 252-261 (2013)",
  "doi": "10.1080/17442508.2011.651215",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\Xi$ be a set of centers chosen according to a Poisson point process in $\\mathbb R^d$. Consider the allocation of $\\mathbb R^d$ to $\\Xi$ which is stable in the sense of the Gale-Shapley marriage problem, with the additional feature that every center $\\xi\\in\\Xi$ has a random appetite $\\alpha V$, where $\\alpha$ is a nonnegative scale constant and $V$ is a nonnegative random variable. Generalizing previous results by Freire, Popov and Vachkovskaia (\\cite{FPV}), we show the absence of percolation when $\\alpha$ is small enough, depending on certain characteristics of the moment of $V$.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2014-04-15T17:49:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05"
    ],
    "keywords": [
      "random appetite",
      "stable marriage",
      "percolation",
      "gale-shapley marriage problem",
      "poisson point process"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.5325A"
    }
  }
}