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 -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 . The main result is a quantitative, non-standard central limit theorem for these random variables as the radius of the balls and the space dimension tend to infinity simultaneously.
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