Identities linking volumes of convex hulls

Advances in Applied Probability

Volumn 39, Issue 3, 2007, Pages 630-644

  Cowan, Richard ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

Author keywords

Convex hull; Random geometry; Sylvester's problem

Indexed keywords

COMPUTATIONAL GEOMETRY; RANDOM PROCESSES; TOPOLOGY;

CONVEX HULL; RANDOM GEOMETRY; SYLVESTER'S PROBLEM;

SET THEORY;

EID: 35948969765     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1189518631     Document Type: Article

References (9)

1. AFFENTRANGER, F. (1988). Generalization of a formula of C. Buchta about the convex hull of random points. Elem. Math. 43, 39-45, 151-152.
2. BADDELEY, A. J. AND MØLLER, J. (1989). Nearest-neighbour Markov point processes and random sets. Internat. Statist. Rev. 57, 89-121.
3. BADDELEY, A. J. AND VAN LIESHOUT, M. N. M. (1995). Area-interaction point processes. Ann. Inst. Statist. Math. 47, 601-619.
4. BADERTSCHER, E. (1989). An explicit formula about the convex hull of random points. Elem. Math. 44, 104-106.
5. BUCHTA, C. (1986). On a conjecture of R. E. Miles about the convex hull of random points. Monatsh. Math. 102, 91-102.
6. BUCHTA, C. (1990). Distribution-independent properties of the convex hull of random points. J. Theoret. Prob. 3, 387-393.
7. GRÜNBAUM, B. (1967). Convex Polytopes. John Wiley, London.
8. MILES, R. E. (1971). Isotropic random simplices. Adv. Appl. Prob. 3, 353-382.
9. STRAUSS, D. J. (1975). A model for clustering. Biometrika 63, 467-475.