paper
A quantitative central limit theorem for Poisson horospheres in high dimensions
Zakhar Kabluchko, Daniel Rosen, Christoph Thäle
A quantitative central limit theorem for Poisson horospheres in high dimensions
Zakhar Kabluchko, Daniel Rosen, Christoph Thäle
paper2023-03-31English
quantitative financearxiv
Description
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.
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