Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-04T19:37:14.505Z Has data issue: false hasContentIssue false
  • English
  • Français

Random paths through convex bodies

Published online by Cambridge University Press:  14 July 2016

Rodney Coleman
Rodney Coleman*
Affiliation:
Imperial College, London
Get access Rights & Permissions [Opens in a new window]

Summary

Several mechanisms under which the randomness of straight line paths through convex bodies can arise are described. Some general results are given relating four of these mechanisms, and the corresponding distributions of the lengths of the straight line paths are found for the circle, the rectangle, and the cube.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 2 , August 1969 , pp. 430 - 441
Copyright
Copyright © Sheffield: Applied Probability Trust 

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

Horowiiz, M. (1965) Probability of random paths across elementary geometrical shapes. J. Appl. Prob. 2, 169–177.CrossRefGoogle Scholar
Horowitz, M. (1966) Correction to HOROWITZ (1965). J. Appl. Prob. 3, Opp. 284.Google Scholar
Kendall, M. G. and Moran, P. A. P. (1963) Geometrical Probability. London, Griffin.Google Scholar
Kingman, J. F. C. (1965) Mean free paths in a convex reflecting region. J. Appl. Prob. 2, 162–168.CrossRefGoogle Scholar
Matern, B. (1960) Spatial variation. Medd. från statens skogsforskningsinstitut 49:5.Google Scholar
Santaló, L. A. (1953) Introduction to Integral Geometry. Paris, Hermann.Google Scholar