{
  "id": "1406.3913",
  "version": "v2",
  "published": "2014-06-16T06:09:53.000Z",
  "updated": "2015-04-05T23:28:02.000Z",
  "title": "Absolute continuity and singularity of Palm measures of the Ginibre point process",
  "authors": [
    "Hirofumi Osada",
    "Tomoyuki Shirai"
  ],
  "comment": "47 pages, version (ii)",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove a dichotomy between absolute continuity and singularity of the Ginibre point process $\\mathsf{G}$ and its reduced Palm measures $\\{\\mathsf{G}_{\\mathbf{x}}, \\mathbf{x} \\in \\mathbb{C}^{\\ell}, \\ell = 0,1,2\\dots\\}$, namely, reduced Palm measures $\\G_{\\mathbf{x}}$ and $\\G_{\\mathbf{y}}$ for $\\mathbf{x} \\in \\mathbb{C}^{\\ell}$ and $\\mathbf{y} \\in \\mathbb{C}^{n}$ are mutually absolutely continuous if and only if $\\ell = n$; they are singular each other if and only if $\\ell \\not= n$. Furthermore, we give an explicit expression of the Radon-Nikodym density $d\\G_{\\mathbf{x}}/d \\G_{\\mathbf{y}}$ for $\\mathbf{x}, \\mathbf{y} \\in \\mathbb{C}^{\\ell}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-16T06:09:53.000Z",
      "abstract": "We prove a dichotomy between absolute continuity and singularity of the Ginibre point process $\\G$ and its reduced Palm measures $\\{\\G_{\\x}, \\x \\in \\c^{\\mm}, \\mm=0,1,2\\dots\\}$, namely, reduced Palm measures $\\G_{\\x}$ and $\\G_{\\y}$ for $\\x \\in \\c^{\\mm}$ and $\\y \\in \\c^{\\nn}$ are mutually absolutely continuous if and only if $\\mm = \\nn$; they are singular if and only if $\\mm \\not= \\nn$. Furthermore, we give an explicit expression of the Radon-Nikodym density $d\\G_{\\x}/d \\G_{\\y}$ for $\\x, \\y \\in \\c^{\\mm}$.",
      "comment": "37 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-05T23:28:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G55",
      "60B20",
      "60K35",
      "82B21",
      "82C22"
    ],
    "keywords": [
      "ginibre point process",
      "absolute continuity",
      "singularity",
      "reduced palm measures",
      "explicit expression"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.3913O"
    }
  }
}