Large cells in Poisson-Delaunay tessellations

Discrete and Computational Geometry

Volumn 31, Issue 4, 2004, Pages 503-514

  Hug, Daniel ^a   Schneider, Rolf ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942560334     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-003-0818-3     Document Type: Article

References (16)

1. A. Goldman, Sur une conjecture de D. G. Kendall concernant la cellule de Crofton du plan et sur sa contrepartie brownienne, Ann. Probab. 26 (1998), 1727-1750.
2. D. Hug, M. Reitzner, and R. Schneider, The limit shape of the zero cell in a stationary Poisson hyperplane tessellation, Ann. Probab. (to appear).
3. I. N. Kovalenko, A proof of a conjecture of David Kendall on the shape of random polygons of large area (Russian), Kibernet. Sistem.Anal. 1997, No. 4, 3-10, 187; Engl. transl. Cybernet. Systems Anal. 33 (1997), 461-467.
4. I. N. Kovalenko, A proof of a conjecture of David Kendall on the shape of random polygons of large area (Russian), Kibernet. Sistem.Anal. 1997, No. 4, 3-10, 187; Engl. transl. Cybernet. Systems Anal. 33 (1997), 461-467.
5. I. N. Kovalenko, An extension of a conjecture of D. G. Kendall concerning shapes of random polygons to Poisson Voronoï cells, In: Voronoï's Impact on Modern Science, Book I (P. Engel, et al., eds.), Transl. from the Ukrainian. Kyiv: Institute of Mathematics, 276 p. Proc. Inst. Math. Natl. Acad. Sci. Ukr. Math. Appl. 212 (1998), 266-274.
6. I. N. Kovalenko, A simplified proof of a conjecture of D. G. Kendall concerning shapes of random polygons, J. Appl. Math. Stochastic Anal. 12 (1999), 301-310.
7. K. Leichtweiß, Über die affine Exzentrizität konvexer Körper, Arch. Math. 10 (1959), 187-199.
8. J. Matoušek, Lectures on Discrete Geometry, Graduate Texts in Mathematics 212, Springer-Verlag, New York, 2002.
9. R. E. Miles, A synopsis of "Poisson flats in Euclidean spaces", Izv. Akad. Nauk Armyan. SSR Mat. 5 (1970), 263-285; reprinted in Stochastic Geometry (E. F. Harding and D. G. Kendall, eds.) Wiley, New York, 1974, pp. 202-227.
10. R. E. Miles, A synopsis of "Poisson flats in Euclidean spaces", Izv. Akad. Nauk Armyan. SSR Mat. 5 (1970), 263-285; reprinted in Stochastic Geometry (E. F. Harding and D. G. Kendall, eds.) Wiley, New York, 1974, pp. 202-227.
11. R. E. Miles, A heuristic proof of a long-standing conjecture of D. G. Kendall concerning the shapes of certain large random polygons, Adv. in Appl. Probab. 27 (1995), 397-417.
12. d, Adv. in Appl. Probab. 21 (1989), 3-73.
13. A. Okabe, B. Boots, K. Sugihara, and S. N. Chiu, Spatial Tessellations; Concepts and Applications of Voronoi Diagrams., 2nd edn., Wiley, Chichester, 2000.
14. R. Schneider, Convex Bodies: the Brunn-Minkowski Theory, Encyclopedia of Mathematics and Its Applications 44, Cambridge University Press, Cambridge, 1993.
15. R. Schneider and W. Weil, Stochastische Geometrie, Teubner Skripten zur Mathematischen Stochastik, Teubner, Stuttgart, 2000.
16. D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and Its Applications, 2nd edn., Wiley, Chichester, 1995.