# Random Inscribing Polytopes

Abstract : For convex bodies $K$ with $\mathcal{C}^2$ boundary in $\mathbb{R}^d$, we provide results on the volume of random polytopes with vertices chosen along the boundary of $K$ which we call $\textit{random inscribing polytopes}$. 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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Communication dans un congrès
Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.263-266, 2005, DMTCS Proceedings
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Littérature citée [15 références]

https://hal.inria.fr/hal-01184448
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• HAL Id : hal-01184448, version 1

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Ross M. Richardson, Van H. Vu, Lei Wu. Random Inscribing Polytopes. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.263-266, 2005, DMTCS Proceedings. 〈hal-01184448〉

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