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Distances in Gaussian point sets

Published online by Cambridge University Press:  24 October 2008

Peter Clifford  and
N. J. B. Green
Peter Clifford
Affiliation:
Mathematical Institute, 24-29 St Giles, Oxford 0X1 3LB
N. J. B. Green
Affiliation:
Physical Chemistry Laboratory, South Parks Road, Oxford
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Abstract

The joint distribution of the n(n− l)/2 distances between n normally distributed points in d dimensions is studied. Moment generating functions and probability density functions are obtained. It is shown that when n = d the squared distances are jointly exponentially distributed subject only to the constraint that a valid n point configuration is prescribed. In the case n = d = 3 the distributions of the ordered distance are obtained explicitly.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 515 - 524
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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