Skip to main contentSkip to search
Episciences
Open Access Journals
Sign in(new window)
Discrete Mathematics & Theoretical Computer Science logo
Discrete Mathematics & Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science logo
Discrete Mathematics & Theoretical Computer Science
Sign in(new window)
Articles & Issues
All articlesAll accepted articlesAll volumesLast volumeSectionsSpecial issuesAuthors
About
The journalIndexing
Boards
Publish
For authorsEthical charter
Submit
Discrete Mathematics & Theoretical Computer Science logo
Contact
|
Credits
eISSN 1365-8050
|
RSS
|
Atom
Episciences
Documentation
|
Acknowledgements
|
Publishing policy
Accessibility: non-compliant
|
Legal mentions
|
Privacy statement
|
Terms of use
  1. Home > Articles & Issues >
  2. Articles >
  3. Random Inscribing Po ...
Conference paper

Random Inscribing Polytopes

Ross M. Richardson (1), van H. Vu, Lei Wu (1)
(1) Department of Mathematics [Univ California San Diego]
Download article
Open on HAL
Imported on
May 10, 2017
Published on
December 31, 2004
Last modified on
March 31, 2025
Volume 0
DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Proceedings
DOI
10.46298/dmtcs.3459
License
https://about.hal.science/hal-authorisation-v1
Indicators
483
Views
597
Downloads

Random Inscribing Polytopes

Ross M. Richardson (1), van H. Vu, Lei Wu (1)
(1) Department of Mathematics [Univ California San Diego]
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.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • random polytope
  • inscribing
  • boundary
  • volume
  • variance
  • central limit theorem
Cited by

Source: OpenCitations

  • Central Limit Theorem for the Volume of Random Polytopes with Vertices on the Boundary

    Discrete & Computational Geometry

    Authors : Christoph Thäle

    Journal reference : Volume 59, 2017, pp. 990-1000

    DOI : 10.1007/s00454-017-9862-2

  • Random inscribed polytopes in projective geometries

    Mathematische Annalen

    Authors : Florian Besau ORCID, Daniel Rosen ORCID, Christoph Thäle

    Journal reference : Volume 381, 2021, pp. 1345-1372

    DOI : 10.1007/s00208-021-02257-9

  • Volume approximation of strongly C -convex domains by random polyhedra

    Advances in Mathematics

    Authors : Siva Athreya ORCID, Purvi Gupta, D. Yogeshwaran

    Journal reference : Volume 432, 2023, pp. 109243

    DOI : 10.1016/j.aim.2023.109243

  • Constrained global sensitivity analysis for bioprocess design space identification

    Spiral (Imperial College London)

    Authors : Pavlos Kotidis ORCID, Panagiotis Demis, Cher H. Goey, Elisa Correa ORCID, Calum McIntosh, Stefania Trepekli, Nilay Shah ORCID, Oleksiy V. Klymenko ORCID, Cleo Kontoravdi ORCID

    Journal reference : Volume 125, 2019, pp. 558-568

    DOI : 10.1016/j.compchemeng.2019.01.022
Preview
Loading PDF preview...