DMTCS Proceedings, 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

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Random Inscribing Polytopes

Ross M. Richardson, Van H. Vu, Lei Wu


For convex bodies K with C2 boundary in ℝd, we provide results on the volume of random polytopes with vertices chosen along the boundary of K which we call random inscribing polytopes. In particular, we prove results concerning the variance and higher moments of the volume, as well as show that the random inscribing polytopes generated by the Poisson process satisfy central limit theorem.

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