Poisson-Delaunay approximation

2024/10/30 by Reitzner, Matthias, Strotmann, Anna · 1 citation
#52B05 #60D05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2410.23003

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_ηt of A is the union of all Delaunay cells generated by η_t with center in A. It is shown that λ_d(A_ηt) 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_ηt) is derived as t →∞.

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