Random Inscribing Polytopes
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2005-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3459/pdf |
| _version_ | 1797270380380946432 |
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| author | Ross M. Richardson Van H. Vu Lei Wu |
| author_facet | Ross M. Richardson Van H. Vu Lei Wu |
| author_sort | Ross M. Richardson |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:03:21Z |
| format | Article |
| id | doaj.art-cfb7869a59c142c8892bc8579bdcd6bb |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:21Z |
| publishDate | 2005-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-cfb7869a59c142c8892bc8579bdcd6bb2024-03-07T14:41:16ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502005-01-01DMTCS Proceedings vol. AE,...Proceedings10.46298/dmtcs.34593459Random Inscribing PolytopesRoss M. Richardson0Van H. VuLei Wu1Department of Mathematics [Univ California San Diego]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.https://dmtcs.episciences.org/3459/pdfrandom polytopeinscribingboundaryvolumevariancecentral limit theorem[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Ross M. Richardson Van H. Vu Lei Wu Random Inscribing Polytopes Discrete Mathematics & Theoretical Computer Science 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] |
| title | Random Inscribing Polytopes |
| title_full | Random Inscribing Polytopes |
| title_fullStr | Random Inscribing Polytopes |
| title_full_unstemmed | Random Inscribing Polytopes |
| title_short | Random Inscribing Polytopes |
| title_sort | random inscribing polytopes |
| topic | 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] |
| url | https://dmtcs.episciences.org/3459/pdf |
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