{
  "id": "math-ph/0212063",
  "version": "v4",
  "published": "2002-12-20T22:08:39.000Z",
  "updated": "2003-09-05T23:12:08.000Z",
  "title": "Janossy Densities I. Determinantal Ensembles",
  "authors": [
    "Alexei Borodin",
    "Alexander Soshnikov"
  ],
  "comment": "This is the first of two papers on Janossy densities in determinantal and pfaffian ensembles. A few misprints are corrected. The paper will appear in J.Stat.Phys, vol. 113, No. 3/4, pp. 595-610 (2003)",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for beta=2 polynomial ensembles of random matrices we show that the Janossy densities on an interval I can be expressed in terms of the Christoffel-Darboux kernel for the orthogonal polynomials on the complement of I.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2003-09-05T23:12:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "janossy densities",
      "determinantal ensembles",
      "finite rank projection-type kernel",
      "determinantal point processes",
      "elementary formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.ph..12063B"
    }
  }
}