Choose n random, independent points in Rd according to the standard normal distribution. Their convex hull Kn is the Gaussian random polytope. We prove that the volume and the number of faces of Kn satisfy the central limit theorem, settling a well-known conjecture in the field.
"Central limit theorems for Gaussian polytopes." Ann. Probab. 35 (4) 1593 - 1621, July 2007. https://doi.org/10.1214/009117906000000791