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Collision probabilities for convex sets

Published online by Cambridge University Press:  14 July 2016

Wolfgang Weil
Wolfgang Weil*
Affiliation:
Universität Karlsruhe
*
∗ Postal address: Mathematisches Institut II, Universität Karlsruhe, Englerstrasse 2, 7500 Karlsruhe 1, West Germany.
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Abstract

Let K, L ⊂ En be non-empty, closed, convex sets, K bounded, and suppose boundary sets αof K and ß of L are painted. If K undergoes a random motion such that K and L touch, the probability for a paint-to-paint contact is expressed by curvature measures of K and L. This generalizes and simplifies previous work of Molter (1986) on infinite cylinders L touching a convex body K.

Keywords

CONTACT PROBABILITIESCURVATURE MEASURESINTEGRAL GEOMETRIC FORMULA

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989, pp. 649 - 654
Copyright
Copyright © Applied Probability Trust 1989 

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References

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