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arXiv · 2410.23003

Poisson-Delaunay approximation

Matthias Reitzner·Anna Strotmann
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Abstract

For a Borel set $A$ and a stationary Poisson point process $η_t$ in $\mathbb R^d$ of intensity $t>0$, the Poisson-Delaunay approximation $ A_{η_t}$ of $A$ is the union of all Delaunay cells generated by $η_t$ with center in $A$. It is shown that $λ_d(A_{η_t})$ is an unbiased estimator for $λ_d(A)$, variance bounds and a quantitative central limit theorem are given. The asymptotic behaviour of the symmetric difference $λ_d(AΔA_{η_t})$ is derived as $t \to\infty$.

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Matthias Reitzner, Anna Strotmann. 2024-10-30. Poisson-Delaunay approximation. https://arxiv.org/abs/2410.23003

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