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Intersections of random hypersurfaces and visibility
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  • Published: September 1986

Intersections of random hypersurfaces and visibility

  • John André Wieacker1 

Probability Theory and Related Fields volume 71, pages 405–433 (1986)Cite this article

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Summary

For a wide class of stationary random hypersurfaces in ℝd the notion of the projection body is introduced. It turns out that this convex body, a very special case of which is Matheron's “Steiner compact” associated with a Poisson process of hyperplanes, contains most of the information concerning certain intersection properties of the random hypersurface, while its polar reciprocal set is closely connected with the behaviour of the random hypersurface in visibility problems. This enables one to give a unified treatment of several intersection and visibility problems for random hypersurfaces. A detailed investigation of the case where the random hypersurface is generated by a Poisson process is given separately.

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Authors and Affiliations

  1. Mathematisches Institut der Universität, Hebelstraße 29, D-7800, Freiburg, Federal Republic of Germany

    John André Wieacker

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  1. John André Wieacker
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Wieacker, J.A. Intersections of random hypersurfaces and visibility. Probab. Th. Rel. Fields 71, 405–433 (1986). https://doi.org/10.1007/BF01000214

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  • Received: 10 October 1984

  • Revised: 18 June 1985

  • Issue Date: September 1986

  • DOI: https://doi.org/10.1007/BF01000214

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Keywords

  • Stochastic Process
  • Probability Theory
  • Poisson Process
  • Mathematical Biology
  • Convex Body
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