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.
References
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Schneider, R.: Inequalities for random flats meeting a convex body. J. Appl. Probab. 22, 710–716 (1985)
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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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DOI: https://doi.org/10.1007/BF00319102
Keywords
- Stochastic Process
- Probability Theory
- Statistical Theory
- Convex Body