We provide a streamlined proof and improved estimates for the weak multivariate Gnedenko law of large numbers on concentration of random polytopes within the space of convex bodies (in a fixed or a high dimensional setting), as well as a corresponding strong law of large numbers.
"Concentration of random polytopes around the expected convex hull." Electron. Commun. Probab. 19 1 - 8, 2014. https://doi.org/10.1214/ECP.v19-3376