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A simulation study of Sylvester's problem in three dimensions

Published online by Cambridge University Press:  14 July 2016

Kim-Anh Do  and
Herbert Solomon
Kim-Anh Do*
Affiliation:
Stanford University
Herbert Solomon*
Affiliation:
Stanford University
*
∗Postal address: Department of Statistics, Stanford University, Sequoia Hall, Stanford, CA 94305, USA.
∗Postal address: Department of Statistics, Stanford University, Sequoia Hall, Stanford, CA 94305, USA.
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Abstract

This note gives estimates of solutions to the Sylvester problem in three dimensions. These results suggest that the solutions in four and higher dimensions are very close to the solution for the n -dimensional sphere which is known.

Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 509 - 513
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

This paper was prepared with the partial support of the Office of Naval Research under Contract N00014–76–C–0475.

References

Hostinsky, B. (1925) Sur les probabilités géométriques. Publ. Fac. Sci. Univ. Masaryk, Brno, Czechoslovakia, 50.Google Scholar
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Solomon, H. (1978) Geometric Probability. CBMS-NSF Regional Conference Series in Applied Mathematics 28, SIAM, Philadelphia.Google Scholar