Facets of high-dimensional Gaussian polytopes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866909067174215680 |
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| author | Boroczky, Karoly J Lugosi, Gabor Reitzner, Matthias |
| author_facet | Boroczky, Karoly J Lugosi, Gabor Reitzner, Matthias |
| contents | We study the number of facets of the convex hull of n independent standard Gaussian points in d-dimensional Euclidean space. In particular, we are interested in the expected number of facets when the dimension is allowed to grow with the sample size. We establish an explicit asymptotic formula that is valid whenever d/n tends to zero. We also obtain the asymptotic value when d is close to n. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_01431 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Facets of high-dimensional Gaussian polytopes Boroczky, Karoly J Lugosi, Gabor Reitzner, Matthias Probability 60D05 secondary: 52A22, 60C05 We study the number of facets of the convex hull of n independent standard Gaussian points in d-dimensional Euclidean space. In particular, we are interested in the expected number of facets when the dimension is allowed to grow with the sample size. We establish an explicit asymptotic formula that is valid whenever d/n tends to zero. We also obtain the asymptotic value when d is close to n. |
| title | Facets of high-dimensional Gaussian polytopes |
| topic | Probability 60D05 secondary: 52A22, 60C05 |
| url | https://arxiv.org/abs/1808.01431 |