Geodesic
Random Inscribing Polytopes
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005).

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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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     author = {Richardson, Ross M. and Vu, Van H. and Wu, Lei},
     title = {Random {Inscribing} {Polytopes}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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     year = {2005},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3459/}
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Richardson, Ross M.; Vu, Van H.; Wu, Lei. Random Inscribing Polytopes. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005). doi : 10.46298/dmtcs.3459. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3459/

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