Abstract
Denote by R m (respectively R M ) the radius of the largest (respectively smallest) disk centered at the origin and included in (respectively containing) the typical cell of the two-dimensional Poisson–Voronoi tessellation. In this article, we obtain the joint distribution of R m and R M . This result is derived from the covering properties of the circle due to Stevens, Siegel and Holst. The computation of the conditional probabilities P {R M⩾r+s∣R m=r} reveals the circular property of the Poisson–Voronoi typical cells having a “large” in-disk. To cite this article: P. Calka, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 325–330.
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