{
  "id": "2306.07732",
  "version": "v1",
  "published": "2023-06-13T12:38:23.000Z",
  "updated": "2023-06-13T12:38:23.000Z",
  "title": "Random analytic functions via Gaussian multiplicative chaos",
  "authors": [
    "Yichao Huang",
    "Eero Saksman"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR",
    "math.CV"
  ],
  "abstract": "We define a random analytic function $\\varphi$ on the unit disc by letting a Gaussian multiplicative measure to be one of its Clark measures. We show that $\\varphi$ is almost surely a Blaschke product and we provide rather sharp estimates for the density of its zeroes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-13T12:38:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random analytic function",
      "gaussian multiplicative chaos",
      "unit disc",
      "blaschke product",
      "sharp estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}