The law of the smallest disk containing the typical Poisson-Voronoi cell (Q1598463)
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scientific article; zbMATH DE number 1744354
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The law of the smallest disk containing the typical Poisson-Voronoi cell |
scientific article; zbMATH DE number 1744354 |
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The law of the smallest disk containing the typical Poisson-Voronoi cell (English)
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4 August 2002
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Let \(R_m\) \((R_M)\) denote the radius of the largest (smallest) disk centered at the origin which is included in (respectively, contains) the typical cell of the two-dimensional Poisson-Voronoi tessellation. Based on covering properties of the circle due to \textit{A. F. Siegel} [J. Appl. Probab. 15, 340-355 (1978; Zbl 0391.60017)] and \textit{A. F. Siegel} and \textit{L. Holst} [ibid. 19, 373-381 (1982; Zbl 0489.60017)] the author obtains the joint distribution of \(R_m\) and \(R_M\).
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two-dimensional Poisson-Voronoi tessellation
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covering properties
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