REAL

Facets of High-Dimensional Gaussian Polytopes

Böröczky, Károly (Ifj.) and Lugosi, Gábor and Reitzner, Matthias (2024) Facets of High-Dimensional Gaussian Polytopes. JOURNAL OF GEOMETRIC ANALYSIS, 34 (3). ISSN 1050-6926

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Abstract

We study the number of facets of the convex hull of n independent standard Gaussian points in Rd . 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 → 0. We also obtain the asymptotic value when d is close to n.

Item Type: Article
Uncontrolled Keywords: Gaussian polytope, Expected number of facets
Subjects: Q Science / természettudomány > QA Mathematics / matematika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 05 Apr 2024 09:10
Last Modified: 05 Apr 2024 09:10
URI: https://real.mtak.hu/id/eprint/191908

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