{
  "id": "0909.0575",
  "version": "v1",
  "published": "2009-09-03T06:11:14.000Z",
  "updated": "2009-09-03T06:11:14.000Z",
  "title": "Geometric Properties of Poisson Matchings",
  "authors": [
    "Alexander E. Holroyd"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Suppose that red and blue points occur as independent Poisson processes of equal intensity in R^d, and that the red points are matched to the blue points via straight edges in a translation-invariant way. We address several closely related properties of such matchings. We prove that there exist matchings that locally minimize total edge length in d=1 and d>=3, but not in the strip R x [0,1]. We prove that there exist matchings in which every bounded set intersects only finitely many edges in d>=2, but not in d=1 or in the strip. It is unknown whether there exists a matching with no crossings in d=2, but we prove positive answers to various relaxations of this question. Several open problems are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-03T06:11:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "60G55",
      "05C70"
    ],
    "keywords": [
      "poisson matchings",
      "geometric properties",
      "independent poisson processes",
      "blue points occur",
      "locally minimize total edge length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.0575H"
    }
  }
}