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Extremal problems for geometric probabilities involving convex bodies

Published online by Cambridge University Press:  01 July 2016

Christina Bauer  and
Rolf Schneider
Christina Bauer*
Affiliation:
Albert-Ludwigs-Universität, Freiburg i. Br.
Rolf Schneider*
Affiliation:
Albert-Ludwigs-Universität, Freiburg i. Br.
*
* Postal address for both authors: Mathematics Institut, Albert-Ludwigs-Universität, Albertstr. 23b, D-79104 Freiburg i. Br., Germany
* Postal address for both authors: Mathematics Institut, Albert-Ludwigs-Universität, Albertstr. 23b, D-79104 Freiburg i. Br., Germany
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Extract

The theory of geometric probabilities is concerned with randomly generated geometric objects. The aim is to compute probabilities of certain geometric events or distributions of random variables defined in a geometric way. Very often the computation even of simple expectations is too difficult, and one has to be satisfied with establishing estimates and, if possible, sharp inequalities. In geometric probabilities, convex sets play a prominent role, since often the convexity assumptions simplify the situation considerably. Extremal problems for geometric probabilities involving convex bodies can sometimes be attacked successfully by using suitable integral-geometric transformations and then applying classical inequalities from the geometry of convex bodies, or known methods for obtaining such inequalities. Examples of such results are the topic of this paper.

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 1 , March 1995 , pp. 20 - 34
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

The original version of this paper was presented at the International Workshop on Stochastic Geometry, Stereology and Image Analysis held at the Universidad Internacional Menendez Pelayo, Valencia, Spain on 21–24 September 1993.

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