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• W2000943710 abstract "A homogeneous Poisson-Voronoi tessellation of intensity γ is observed in a convex body W. We associate to each cell of the tessellation two characteristic radii: the inradius, i.e. the radius of the largest ball centered at the nucleus and included in the cell, and the circumscribed radius, i.e. the radius of the smallest ball centered at the nucleus and containing the cell. We investigate the maximum and minimum of these two radii over all cells with nucleus in W. We prove that when $gamma rightarrow infty $ , these four quantities converge to Gumbel or Weibull distributions up to a rescaling. Moreover, the contribution of boundary cells is shown to be negligible. Such approach is motivated by the analysis of the global regularity of the tessellation. In particular, consequences of our study include the convergence to the simplex shape of the cell with smallest circumscribed radius and an upper-bound for the Hausdorff distance between W and its so-called Poisson-Voronoi approximation." @default.
• W2000943710 created "2016-06-24" @default.
• W2000943710 creator A5038227564 @default.
• W2000943710 creator A5051812566 @default.
• W2000943710 date "2014-05-02" @default.
• W2000943710 modified "2023-10-16" @default.
• W2000943710 title "Extreme values for characteristic radii of a Poisson-Voronoi Tessellation" @default.
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• W2000943710 doi "https://doi.org/10.1007/s10687-014-0184-y" @default.
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