Variance Asymptotics and Scaling Limits for Gaussian Polytopes
نویسندگان
چکیده
Let Kn be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on Rd. We establish variance asymptotics for the re-scaled volume and k-face functional of Kn, k ∈ {0, 1, ..., d − 1}, resolving an open problem. Asymptotic variances and the scaling limit of the boundary of Kn are given in terms of functionals of germ-grain models having parabolic grains with apices at a Poisson point process on Rd−1 × R with intensity ehdhdv. 1 Main results For all λ ∈ (0,∞), let Pλ denote a Poisson point process of intensity λφ(x)dx, where φ(x) := (2π)−d/2 exp(−|x| 2
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