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Random secants of a convex body

Published online by Cambridge University Press:  14 July 2016

J. F. C. Kingman
J. F. C. Kingman*
Affiliation:
University of Sussex
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Summary

Let two points be taken at random in an n-dimensional convex body K, and let σ be the line joining them. The distribution of σ is found and compared with other distributions for random secants of K. More generally, if r + 1 ≦ npoints are taken in K, the distribution of the r-dimensional affine subspace containing them is computed. The results find application to the n-dimensional case of a problem of Sylvester.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 660 - 672
Copyright
Copyright © Applied Probability Trust 

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References

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