Facets of high-dimensional Gaussian polytopes

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  • dc.contributor.author Böröczky, Károly J.
  • dc.contributor.author Lugosi, Gábor
  • dc.contributor.author Reitzner, Matthias
  • dc.date.accessioned 2025-06-17T14:33:53Z
  • dc.date.available 2025-06-17T14:33:53Z
  • dc.date.issued 2024
  • dc.date.updated 2025-06-17T14:33:52Z
  • dc.description.abstract 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.
  • dc.description.sponsorship K. Böröczky research was supported by Hungarian Grant NKFIH 132002. G. Lugosi research was supported by the Spanish grant PID2022-138268NB-I00, financed by MCIN/AEI/10.13039/501100011033, FSE+MTM2015-67304-P, and FEDER, EU. M. Reitzner research was supported by the German Research Foundation DFG-GRK 1916.
  • dc.format.mimetype application/pdf
  • dc.identifier.citation Böröczky KJ, Lugosi G, Reitzner M. Facets of high-dimensional Gaussian polytopes. J Geom Anal. 2024;34:69. DOI: 10.1007/s12220-023-01440-5
  • dc.identifier.doi http://dx.doi.org/10.1007/s12220-023-01440-5
  • dc.identifier.issn 1050-6926
  • dc.identifier.uri http://hdl.handle.net/10230/70705
  • dc.language.iso eng
  • dc.publisher Springer
  • dc.relation.ispartof Journal of Geometric Analysis. 2024;34:69
  • dc.relation.projectID info:eu-repo/grantAgreement/ES/3PE/PID2022-138268NB-I00
  • dc.rights This 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/.
  • dc.rights.accessRights info:eu-repo/semantics/openAccess
  • dc.rights.uri http://creativecommons.org/licenses/by/4.0/
  • dc.subject.keyword Gaussian polytope
  • dc.subject.keyword Expected number of facets
  • dc.title Facets of high-dimensional Gaussian polytopes
  • dc.type info:eu-repo/semantics/article
  • dc.type.version info:eu-repo/semantics/publishedVersion

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