{
  "id": "2303.17827",
  "version": "v1",
  "published": "2023-03-31T06:49:15.000Z",
  "updated": "2023-03-31T06:49:15.000Z",
  "title": "A quantitative central limit theorem for Poisson horospheres in high dimensions",
  "authors": [
    "Zakhar Kabluchko",
    "Daniel Rosen",
    "Christoph Thäle"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.PR",
    "math.MG"
  ],
  "abstract": "Consider a stationary Poisson process of horospheres in a $d$-dimensional hyperbolic space. In the focus of this note is the total surface area these random horospheres induce in a sequence of balls of growing radius $R$. The main result is a quantitative, non-standard central limit theorem for these random variables as the radius $R$ of the balls and the space dimension $d$ tend to infinity simultaneously.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-31T06:49:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A55",
      "60D05",
      "60F05",
      "60G55"
    ],
    "keywords": [
      "quantitative central limit theorem",
      "high dimensions",
      "poisson horospheres",
      "non-standard central limit theorem",
      "random horospheres induce"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}