Random Laguerre tessellations

Advances in Applied Probability

Volumn 40, Issue 3, 2008, Pages 630-650

  Lautensack, Claudia ^a,b   Zuyev, Sergei ^c  

^a UNIVERSITY OF APPLIED SCIENCES   (Germany)

^b FRAUNHOFER INSTITUTE FOR INDUSTRIAL MATHEMATICS ITWM   (Germany)

^c UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

K face density; Laguerre tessellation; Poisson process; Power tessellation; Random tessellation; Stochastic geometry; Weighted Voronoi tessellation

Indexed keywords

DISTRIBUTION FUNCTIONS; GEOMETRY; GRAIN SIZE AND SHAPE; POISSON EQUATION; RANDOM PROCESSES;

K-FACE DENSITY; LAGUERRE TESSELLATION; POISSON PROCESS; POWER TESSELLATION; RANDOM TESSELLATION; STOCHASTIC GEOMETRY; WEIGHTED VORONOI TESSELLATION;

POISSON DISTRIBUTION;

EID: 48749114146     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1222868179     Document Type: Article

References (24)

1. ASH, P. AND BOLKER, E.(1986). Generalized Dirichlet tessellations. Geometriae Dedicata 20, 230-243.
2. d+1. Discrete Computational Geometry 2, 49-64.
3. AURENHAMMER, F.(1987). Power diagrams: properties, algorithms and applications. SIAM J. Comput. 16, 78-96.
4. BARNDORFF-NIELSEN, O., KENDALL, W. AND VAN LIESHOUT, M.(1999). Stochastic Geometry Likelihood and Computation. Chapman & Hall/CRC, Boca Raton, FL.
5. BAUMSTARK, V. AND LAST, G.(2007). Some distributional results for Poisson-Voronoi tessellations. Adv. Appl. Prob. 39, 16-40.
6. BLASCHKE, W.(1929). Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. Springer, Berlin.
7. BOISSONNAT, J.-D. AND YVINEC, M.(1998). Algorithmic Geometry. Cambridge University Press.
8. COXETER, H. S. M.(1969). Introduction to Geometry. John Wiley, New York.
9. FISCHER, W., KOCH, E. AND HELLNER, E.(1971). Zur Berechnung von Wirkungsbereichen in Strukturen anorganischer Verbindungen. Neues Jahrbuch für Mineralogie Monatshefte 1971, 227-237.
10. HEINRICH, L.(1998). Contact and chord length distribution of a stationary Voronoi tessellation. Adv. Appl. Prob. 30, 603-618.
11. IMAI, H., IRI, M. AND MUROTA, K.(1985). Voronoi diagram in the Laguerre geometry and its applications. SIAM J. Comput. 14, 93-105.
12. LAUTENSACK, C.(2007). Random Laguerre tessellations. Lautensack, Weiler bei Bingen. Available at http://www.itwm.fhg.de/bv/ theses/works/lautensack.
13. MECKE, J.(1984). Parametric representation of mean values for stationary random mosaics. Math. Operat. Statist. Ser. Statist. 3, 437-442.
14. MILES, R. E.(1971). Isotropic random simplices. Adv. Appl. Prob. 3, 353-382.
15. MOLCHANOV, I.(2005). Theory of Random Sets. Springer, Berlin.
16. d. Adv. Appl. Prob. 21, 37-73.
17. MØLLER, J.(1992). Random Johnson-Mehl tessellations. Adv. Appl. Prob. 24, 814-844.
18. MØLLER, J.(1994). Lectures on Random Voronoi Tessellations (Lecture Notes Statist. 87). Springer, New York.
19. MUCHE, L. AND STOYAN, D.(1992). Contact and chord length distributions of the Poisson-Voronoi tessellation. J. Appl. Prob. 29, 467-471.
20. OKABE, A., BOOTS, B., SUGIHARA, K. AND CHIU, S. N.(2000). Spatial Tessellations - Concepts and Applications of Voronoi Diagrams, 2nd edn. John Wiley, Chichester.
21. SCHLOTTMANN, M.(1993). Periodic and quasi-periodic Laguerre tilings. Internat. J. Modern Phys. B 7, 1351-1363.
22. SCHNEIDER, R.(1993). Convex Bodies: The Brunn-Minkowski Theory. Cambridge University Press.
23. SCHNEIDER, R. AND WEIL, W.(1992). Integralgeometrie. Teubner, Stuttgart.
24. SCHNEIDER, R. AND WEIL, W.(2000). Stochastische Geometrie. Teubner, Leipzig.