A simplified proof of a conjecture of D.G. Kendall concerning shapes of random polygons

Journal of Applied Mathematics and Stochastic Analysis

Volumn 12, Issue 4, 1999, Pages 301-310

  Kovalenko, Igor N ^a  

^a V M GLUSHKOV INSTITUTE OF CYBERNETICS   (Ukraine)

Author keywords

Random Sets; Random Tessellation; Stochastic Geometry

Indexed keywords

EID: 0012483780     PISSN: 10489533     EISSN: 16872177     Source Type: Journal    
DOI: 10.1155/S1048953399000283     Document Type: Article

References (6)

1. Bonnesen, T., Über eine Vershärfung der isoperimetrischen Ungleichheit des Kreises in der Ebene und auf der Kugeloberflache nebst einer Anwendung auf eine Minkowskische Ungleichheit für konvexe Körper, Math. Ann. 84 (1921), 216-227.
2. Goldman, A., Sur une conjecture de D.G. Kendall concernant la cellule de Crofton du plan et sur sa contrepartie brownienne, Compt. Rend. Acad. Sci. Paris 326:1 (1998), 233-237.
3. Kovalenko, I.N., An alternative approach to R.E. Miles' proof of a conjecture of D.G. Kendall concerning the shapes of random polygons, Doc. No. 62810, STORM, University of North London (1997).
4. Kovalenko, I.N., Proof of David Kendall's conjecture concerning the shape of large random polygons, Cybern, and Sys. Anal. 33:4 (1997), 461-467.
5. Miles, R.E., A heuristic proof a long-standing conjecture of D.G. Kendall concerning the shapes of certain large random polygons, Adv. Appl. Prob. (SGSA) 27 (1997), 397-471.
6. Stoyan, D., Kendall, W.S., Mecke, J., Stochastic Geometry and Its Applications, With a Forward by D.G. Kendall, John Wiley and Sons, New York 1987.