{
  "id": "1703.08978",
  "version": "v1",
  "published": "2017-03-27T09:18:38.000Z",
  "updated": "2017-03-27T09:18:38.000Z",
  "title": "Equivalence of Palm measures for determinantal point processes governed by Bergman kernels",
  "authors": [
    "Alexander I. Bufetov",
    "Shilei Fan",
    "Yanqi Qiu"
  ],
  "comment": "31 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.DS",
    "math.FA",
    "math.MP"
  ],
  "abstract": "For a determinantal point process induced by the reproducing kernel of the weighted Bergman space $A^2(U, \\omega)$ over a domain $U \\subset \\mathbb{C}^d$, we establish the mutual absolute continuity of reduced Palm measures of any order provided that the domain $U$ contains a non-constant bounded holomorphic function. The result holds in all dimensions. The argument uses the $H^\\infty(U)$-module structure of $A^2(U, \\omega)$. A corollary is the quasi-invariance of our determinantal point process under the natural action of the group of compactly supported diffeomorphisms of $U$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-27T09:18:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "determinantal point process",
      "bergman kernels",
      "equivalence",
      "mutual absolute continuity",
      "non-constant bounded holomorphic function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}