{
  "id": "1605.01400",
  "version": "v1",
  "published": "2016-05-04T19:51:46.000Z",
  "updated": "2016-05-04T19:51:46.000Z",
  "title": "Conditional measures of determinantal point processes",
  "authors": [
    "Alexander I. Bufetov"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.DS",
    "math.MP"
  ],
  "abstract": "For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the configuration in the complement of a compact interval, are orthogonal polynomial ensembles with explicitly found weights. Examples include the sine-process and the process with the Bessel kernel. The argument uses the quasi-invariance, established in [1], of our point processes under the group of piecewise isometries of the real line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-04T19:51:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G55",
      "60G09",
      "60G30",
      "37A50",
      "37A40"
    ],
    "keywords": [
      "conditional measures",
      "one-dimensional determinantal point processes",
      "orthogonal polynomial ensembles",
      "growth condition",
      "compact interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}