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1 results

  • Stochastic geometry from the standpoint of integral geometry

  • R. V. Ambartzumian
  • Journal:
    Advances in Applied Probability / Volume 9 / Issue 4 / December 1977
    Published online by Cambridge University Press:
    01 July 2016, pp. 792-823
    Print publication:
    December 1977

  • 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.