• Medientyp: E-Artikel
  • Titel: Random Laguerre tessellations
  • Beteiligte: Lautensack, Claudia; Zuyev, Sergei
  • Erschienen: Cambridge University Press (CUP), 2008
  • Erschienen in: Advances in Applied Probability, 40 (2008) 3, Seite 630-650
  • Sprache: Englisch
  • DOI: 10.1239/aap/1222868179
  • ISSN: 0001-8678; 1475-6064
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  • Beschreibung: A systematic study of random Laguerre tessellations, weighted generalisations of the well-known Voronoi tessellations, is presented. We prove that every normal tessellation with convex cells in dimension three and higher is a Laguerre tessellation. Tessellations generated by stationary marked Poisson processes are then studied in detail. For these tessellations, we obtain integral formulae for geometric characteristics and densities of the typical k-faces. We present a formula for the linear contact distribution function and prove various limit results for convergence of Laguerre to Poisson-Voronoi tessellations. The obtained integral formulae are subsequently evaluated numerically for the planar case, demonstrating their applicability for practical purposes.