
























Abstract:We determine analytically for all $k\in\{0,1,\ldots,d-1\}$ the $k$-volume densities of a Poisson--Voronoi tessellation of intensity $\lambda>0$ in the $d$-dimensional hyperbolic space of constant curvature $-1$. This largely extends previous results of Isokawa in dimensions two and three. As applications, we provide closed form expressions for all face volume densities and all typical face volumes of the ideal Poisson--Voronoi tessellation (IPVT), which is the low-intensity limit as $\lambda\downarrow0$ of the hyperbolic Poisson--Voronoi tessellation. As a main tool we develop a new Blaschke--Petkantschin--type formula in hyperbolic space.
From: Matteo D'Achille [view email]
[v1]
Wed, 24 Jun 2026 17:27:08 UTC (1,239 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。