Sie können Bookmarks mittels Listen verwalten, loggen Sie sich dafür bitte in Ihr SLUB Benutzerkonto ein.
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
Entstehung:
Anmerkungen:
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.