Published October 2022
| public
Journal Article
Facets of spherical random polytopes
- Creators
- Bonnet, Gilles
- O'Reilly, Eliza
Abstract
Facets of the convex hull of n independent random vectors chosen uniformly at random from the unit sphere in ℝᵈ are studied. A particular focus is given on the height of the facets as well as the expected number of facets as the dimension increases. Regimes for n and d with different asymptotic behavior of these quantities are identified and asymptotic formulas in each case are established. Extensions of several known results in fixed dimension to the case where dimension tends to infinity are described.
Additional Information
The first named author was partially supported by the DFG priority program SPP 2265: Random Geometric Systems. The second named author was supported by a grant of the Simons Foundation (#197982 to UT Austin).Additional details
- Eprint ID
- 117473
- Resolver ID
- CaltechAUTHORS:20221017-15547800.36
- SPP 2265
- Deutsche Forschungsgemeinschaft (DFG)
- 197982
- Simons Foundation
- Created
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2022-10-25Created from EPrint's datestamp field
- Updated
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2022-10-25Created from EPrint's last_modified field