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The Extremal Index for a Random Tessellation

  • Nicolas ChenavierEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)

Abstract

Let \(m\) be a random tessellation in \(\mathbf {R}^d\), \(d\ge 1\), observed in the window \(\mathbf {W}_{\!\rho }=\rho ^{1/d}[0,1]^d\), \(\rho >0\), and let f be a geometrical characteristic. We investigate the asymptotic behaviour of the maximum of f(C) over all cells \(C\in m\) with nucleus in \(\mathbf {W}_{\!\rho }\) as \(\rho \) goes to infinity. When the normalized maximum converges, we show that its asymptotic distribution depends on the so-called extremal index. Two examples of extremal indices are provided for Poisson-Voronoi and Poisson-Delaunay tessellations.

Keywords

Random tessellations Extreme values Poisson point process 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Université du Littoral Côte D’OpaleCalaisFrance

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