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Equiaffine inner parallel curves of a plane convex body and the convex hulls of randomly chosen points
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  • Published: July 1997

Equiaffine inner parallel curves of a plane convex body and the convex hulls of randomly chosen points

  • Christian Buchta1 &
  • Matthias Reitzner1 

Probability Theory and Related Fields volume 108, pages 385–415 (1997)Cite this article

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  • 18 Citations

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Summary.

A general formula is proved, which relates the equiaffine inner parallel curves of a plane convex body and the probability that the convex hull of j independent random points is disjoint from the convex hull of k further independent random points. This formula is applied to improve some well-known results in geometric probability. For example, an estimate, which was established for a special case by L. C. G. Rogers, is obtained with the best possible bound, and an asymptotic formula due to A. Rényi and R.␣Sulanke is extended to an asymptotic expansion.

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  1. Institut für Analysis, Technische Mathematik und Versicherungsmathematik, Technische Universität, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria, , , , , , AT

    Christian Buchta & Matthias Reitzner

Authors
  1. Christian Buchta
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  2. Matthias Reitzner
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Received: 21 May 1996

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Buchta, C., Reitzner, M. Equiaffine inner parallel curves of a plane convex body and the convex hulls of randomly chosen points. Probab Theory Relat Fields 108, 385–415 (1997). https://doi.org/10.1007/s004400050114

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  • Issue Date: July 1997

  • DOI: https://doi.org/10.1007/s004400050114

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  • Mathematics Subject Classification(1991): 52A22 60D05
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