{
  "id": "1110.6333",
  "version": "v1",
  "published": "2011-10-28T13:49:31.000Z",
  "updated": "2011-10-28T13:49:31.000Z",
  "title": "Lipschitz correspondence between metric measure spaces and random distance matrices",
  "authors": [
    "Siddhartha Gadgil",
    "Manjunath Krishnapur"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR",
    "math.MG"
  ],
  "abstract": "Given a metric space with a Borel probability measure, for each integer $N$ we obtain a probability distribution on $N\\times N$ distance matrices by considering the distances between pairs of points in a sample consisting of $N$ points chosen indepenedently from the metric space with respect to the given measure. We show that this gives an asymptotically bi-Lipschitz relation between metric measure spaces and the corresponding distance matrices. This is an effective version of a result of Vershik that metric measure spaces are determined by associated distributions on infinite random matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-28T13:49:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric measure spaces",
      "random distance matrices",
      "lipschitz correspondence",
      "metric space",
      "infinite random matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.6333G"
    }
  }
}