English

A quantitative central limit theorem for Poisson horospheres in high dimensions

Probability 2024-03-08 v2 Metric Geometry

Abstract

Consider a stationary Poisson process of horospheres in a dd-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 RR. The main result is a quantitative, non-standard central limit theorem for these random variables as the radius RR of the balls and the space dimension dd tend to infinity simultaneously.

Keywords

Cite

@article{arxiv.2303.17827,
  title  = {A quantitative central limit theorem for Poisson horospheres in high dimensions},
  author = {Zakhar Kabluchko and Daniel Rosen and Christoph Thäle},
  journal= {arXiv preprint arXiv:2303.17827},
  year   = {2024}
}

Comments

10 pages, 1 figure

R2 v1 2026-06-28T09:42:31.164Z