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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference28 articles.
1. Kendall D. G. (1974) An introduction to stochastic geometry. In Harding and Kendall [17].
2. The various aggregates of random polygons determined by random lines in a plane
3. Homogeneous and isotropic random fibrefields on the plane (in Russian);Ambartzumian;Izv. Akad. Nauk Armjan SSR Ser. Mat.,1975
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