Poisson-Delaunay approximation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912096025837568 |
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| author | Reitzner, Matthias Strotmann, Anna |
| author_facet | Reitzner, Matthias Strotmann, Anna |
| contents | 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 $t \to\infty$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_23003 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poisson-Delaunay approximation Reitzner, Matthias Strotmann, Anna Probability 52B05, 60D05 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 $t \to\infty$. |
| title | Poisson-Delaunay approximation |
| topic | Probability 52B05, 60D05 |
| url | https://arxiv.org/abs/2410.23003 |