Facets of High-Dimensional Gaussian Polytopes

We study the number of facets of the convex hull of n independent standard Gaussian points in ℝ^d . 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 .