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Stochastic geometry from the standpoint of integral geometry

Published online by Cambridge University Press:  01 July 2016

R. V. Ambartzumian
R. V. Ambartzumian*
Affiliation:
Institute of Mathematics, Armenian Academy of Sciences, Erevan, Armenian SSR
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Abstract

This two-part paper surveys some recent developments in integral and stochastic geometry. Part I surveys applications of integral geometry to the theory of euclidean motion-invariant random fibrefields (a fibrefield is a collection of smooth arcs on the plane), involving marked point processes, Palm distribution theory and vertex pattern analysis. Part II develops the more sophisticated theory of Buffon sets in stochastic geometry and the characterisation of measures of lines, giving applications to problems concerning random triangles and colourings, line processes and fixed convex sets.

Keywords

STOCHASTIC AND INTEGRAL GEOMETRYRANDOM FIBREFIELDSBUFFON'S NEEDLE PROBLEMBUFFON-SYLVESTER PROBLEMPALM DISTRIBUTIONSMARKED POINT PROCESSESBUFFON RINGS AND BUFFON SETSRANDOM TRIANGLESRANDOM COLOURINGS
Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 4 , December 1977 , pp. 792 - 823
Copyright
Copyright © Applied Probability Trust 1977 

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References

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