Facets of High-Dimensional Gaussian Polytopes

Open Access
  • Authors: Gábor Lugosi.
  • Statistics
  • The Journal of Geometric Analysis
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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 growwith 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.

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