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Facets of high-dimensional Gaussian polytopes

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 نشر من قبل Karoly J. Boroczky
 تاريخ النشر 2018
  مجال البحث
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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.



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