The law of the smallest disk containing the typical Poisson-Voronoi cell
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 \(R_M\).
two-dimensional Poisson-Voronoi tessellation
scientific article; zbMATH DE number 1744354