Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T20:07:43.485Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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