{
  "id": "1806.02306",
  "version": "v1",
  "published": "2018-06-06T17:10:09.000Z",
  "updated": "2018-06-06T17:10:09.000Z",
  "title": "Patterson-Sullivan measures for point processes and the reconstruction of harmonic functions",
  "authors": [
    "Alexander I. Bufetov",
    "Yanqi Qiu"
  ],
  "comment": "57 pages",
  "categories": [
    "math.PR",
    "math.DS",
    "math.FA",
    "math.MG"
  ],
  "abstract": "The Patterson-Sullivan construction is proved almost surely to recover every Hardy function from its values on the zero set of a Gaussian analytic function on the disk. The argument relies on the conformal invariance and the slow growth of variance of the linear statistics for the underlying point process. Patterson-Sullivan reconstruction of Hardy functions is obtained in real and complex hyperbolic spaces of arbitrary dimension, while reconstruction of continuous functions is shown to hold in general $\\mathrm{CAT}(-1)$ spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-06T17:10:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "point process",
      "harmonic functions",
      "patterson-sullivan measures",
      "hardy function",
      "gaussian analytic function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}