{
  "id": "1011.4043",
  "version": "v2",
  "published": "2010-11-17T20:18:57.000Z",
  "updated": "2016-05-01T18:42:45.000Z",
  "title": "A note about the uniform distribution on the intersection of a simplex and a sphere",
  "authors": [
    "Sourav Chatterjee"
  ],
  "comment": "21 pages. To appear in J. Topol. Anal",
  "categories": [
    "math.PR"
  ],
  "abstract": "Uniform probability distributions on $\\ell_p$ balls and spheres have been studied extensively and are known to behave like product measures in high dimensions. In this note we consider the uniform distribution on the intersection of a simplex and a sphere. Certain new and interesting features, such as phase transitions and localization phenomena emerge.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-17T20:18:57.000Z",
      "comment": "22 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-05-01T18:42:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "82B26",
      "82B10",
      "60F10"
    ],
    "keywords": [
      "uniform distribution",
      "intersection",
      "uniform probability distributions",
      "localization phenomena emerge",
      "product measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.4043C"
    }
  }
}