Year: 2025
Type: preprint
Abstract: We consider Gaussian approximation in three particular models of Poisson-Laguerre tessellations, namely, the $β$-, $β'$- and Gaussian-Voronoi tessellations. The tessellations are constructed based on inhomogeneous Poisson point processes in space-time $\mathbb{R}^d \times \mathbb{R}$, where some of the points of the process give rise to a cell in $\mathbb{R}^d$, known as extreme points, while the other points produce an empty cell. Using the notion of region-stabilization, we derive quantitative central limit theorems with presumably optimal rates of convergence for the number of extreme points of $β$-, $β'$- and Gaussian-Voronoi tessellations in a growing window $W_n=[-n,n]^d$ as $n\to\infty$. Our bounds improve and extend previously known results by Schreiber and Yukich (2008) for the $β$-model, and are the first quantitative results for the $β'$- and Gaussian models.
Source: arXiv (Cornell University)
Authors: Bhattacharjee, Chinmoy, Gusakova, Anna
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417328501
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