Ross M. Richardson ; Van H. Vu ; Lei Wu - Random Inscribing Polytopes

dmtcs:3459 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) - https://doi.org/10.46298/dmtcs.3459
Random Inscribing Polytopes

Authors: Ross M. Richardson 1; Van H. Vu ; Lei Wu 1

  • 1 Department of Mathematics [Univ California San Diego]

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.


Volume: DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: random polytope,inscribing,boundary,volume,variance,central limit theorem,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo ARXIV 2203.12444
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.2203.12444
  • 10.48550/arxiv.2203.12444
  • 2203.12444
Volume Approximation of Strongly ${\mathbb C}$-Convex Domains by Random Polyhedra

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