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Facets of spherical random polytopes

Bonnet, Gilles and O'Reilly, Eliza (2022) Facets of spherical random polytopes. Mathematische Nachrichten, 295 (10). pp. 1901-1933. ISSN 0025-584X. doi:10.1002/mana.202000314.

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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.

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Bonnet, Gilles0000-0003-4161-4124
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).
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)SPP 2265
Simons Foundation197982
Issue or Number:10
Record Number:CaltechAUTHORS:20221017-15547800.36
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117473
Deposited By: Research Services Depository
Deposited On:25 Oct 2022 19:55
Last Modified:25 Oct 2022 19:55

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