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Pairs of non-intersecting random flats
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  • Published: September 1988

Pairs of non-intersecting random flats

  • F. Affentranger1 

Probability Theory and Related Fields volume 79, pages 47–49 (1988)Cite this article

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  • 2 Citations

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Summary

Let A r,A s,1≦r+s≦n-1, be independent isotropic uniform random r- resp. s-flats meeting a n-dimensional convex body K. It is shown that the probability that the points realizing the distance of A rand A sbelong to K is maximal if and only if K is a ball.

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References

  1. Knothe, H.: Über Ungleichungen bei Sehnenpotenzintegralen. Deutsche Math. 2, 544–551 (1937)

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  2. Petkantschin, B.: Zusammenhänge zwischen den Dichten der linearen Unterräume im n-dimensionalen Raum. Abh. Math. Sem. Univ. Hamburg 11, 249–310 (1936)

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  3. Santaló, L.A.: Integral geometry and geometric probability. Reading, Mass.: Addison-Wesley 1976

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  4. Schneider, R.: Inequalities for random flats meeting a convex body. J. Appl. Probab. 22, 710–716 (1985)

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Author information

Authors and Affiliations

  1. Departmento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428, Buenos Aires, Argentina

    F. Affentranger

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  1. F. Affentranger
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Cite this article

Affentranger, F. Pairs of non-intersecting random flats. Probab. Th. Rel. Fields 79, 47–49 (1988). https://doi.org/10.1007/BF00319102

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  • Received: 04 December 1987

  • Revised: 18 March 1988

  • Issue Date: September 1988

  • DOI: https://doi.org/10.1007/BF00319102

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Convex Body
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