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  • 1 Alfréd Rényi Institute of Mathematics H-1364 Budapest P. O. Box: 127 Hungary
  • 2 Technische Universität Wien Institut für Diskrete Mathematik und Geometrie Wiedner Hauptstr. 8-10 A-1040 Wien Austria
  • 3 Universität Karlsruhe (TH), KIT Institut für Algebra und Geometrie D-76133 Karlsruhe Germany
  • 4 Eötvös Loránd University Department of Geometry Pázmány Péter sétány 1/C H-1117 Budapest Hungary
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Abstract  

Let K be a convex body in ℝd, let j ∈ {1, …, d−1}, and let K(n) be the convex hull of n points chosen randomly, independently and uniformly from K. If ∂K is C+2, then an asymptotic formula is known due to M. Reitzner (and due to I. Bárány if ∂K is C+3) for the difference of the jth intrinsic volume of K and the expectation of the jth intrinsic volume of K(n). We extend this formula to the case when the only condition on K is that a ball rolls freely inside K.

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