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Random spherical triangles II: Shape densities

Published online by Cambridge University Press:  01 July 2016

Huiling Le
Huiling Le*
Affiliation:
University of Cambridge
*
∗Postal address: Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB, UK.
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Abstract

This paper gives the exact evaluation of the shape density on the shape space Σ(S2, 3) for a labelled random spherical triangle whose vertices are i.i.d.-uniform in a ‘cap' of S2 bounded by a ‘small' circle of angular radius ρ0.

Keywords

COLLINEARITYINVARIANT MEASUREQUASARSRANDOM SPHERICAL TRIANGLEREFLECTING BROWNIAN MOTIONSINGULAR TESSELLATIONSIZE-AND-SHAPE SPACEVOLUME MEASURE
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 3 , September 1989 , pp. 581 - 594
Copyright
Copyright © Applied Probability Trust 1989 

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References

[1] Carne, T. K. (1988) The shape space for points on the sphere. Submitted to Proc. London Math. Soc. Google Scholar
[2] Kendall, D. G. (1984) Shape-manifolds, procrustean metrics, and complex projective spaces. Bull. Lond. Math. Soc. 16, 81–121.Google Scholar
[3] Kendall, D. G. (1988) A survey of the statistical theory of shape. Statistical Science. To appear.Google Scholar
[4] Kendall, D. G. (1988) Spherical triangles revisited. In preparation.Google Scholar
[5] Le, H. (1988) Shape Theory in Flat and Curved Spaces, and Shape Densities with Uniform Generators. Ph.D. Dissertation, Statistical Laboratory, University of Cambridge.Google Scholar
[6] Le, H. (1989) Random spherical triangles I: geometrical background. Adv. Appl. Prob. 21, 580–590.Google Scholar