Böröczky, Károly J.Lugosi, GáborReitzner, Matthias2025-06-172025-06-172024Böröczky KJ, Lugosi G, Reitzner M. Facets of high-dimensional Gaussian polytopes. J Geom Anal. 2024;34:69. DOI: 10.1007/s12220-023-01440-51050-6926http://hdl.handle.net/10230/70705We 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.application/pdfengThis article is licensed under a CreativeCommonsAttribution 4.0 InternationalLicense, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.info:eu-repo/semantics/article2025-06-17http://dx.doi.org/10.1007/s12220-023-01440-5Gaussian polytopeExpected number of facetsinfo:eu-repo/semantics/openAccess