Central limit theorems for Gaussian polytopes

I. Barany; V. H. Vu

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Central limit theorems for Gaussian polytopes

I. Barany·V. H. Vu

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Abstract

Choose $n$ random, independent points in $\R^d$ according to the standard normal distribution. Their convex hull $K_n$ is the {\sl Gaussian random polytope}. We prove that the volume and the number of faces of $K_n$ satisfy the central limit theorem, settling a well known conjecture in the field.

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I. Barany, V. H. Vu. 2006-10-05. Central limit theorems for Gaussian polytopes. https://arxiv.org/abs/math/0610192

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