Central limit theorems for Gaussian polytopes

Details Central limit theorems for Gaussian polytopes Central limit theorems for Gaussian polytopes

2006-10-05

arxiv.org/abs/math/0610192v1

Mathematics

Combinatorics

to appear in Annals of Probability

Scientific paper

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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