Summary
The number of edges A n , the length l n and the surface F n of the convex hull of n independent, identically distributed random points in the plane are considered under the assumption of rotational symmetry. The asymptotic behaviour of the expectations E(A n ), E(l n ) and E(F n ) is studied according to the behaviour of the function Pr(\(Pr{\text{(}}\overline {OP} > x{\text{) as }}x \to {\text{1}}\) as x → 1 (distributions on the unit disc) or x→∞ (distributions on the whole plane).
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Literatur
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Herrn Prof. H. Hadwiger zu seinem 60. Geburtstag gewidmet.
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Carnal, H. Die konvexe Hülle von n rotationssymmetrisch verteilten Punkten. Z. Wahrscheinlichkeitstheorie verw Gebiete 15, 168–176 (1970). https://doi.org/10.1007/BF00531885
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DOI: https://doi.org/10.1007/BF00531885