This is an announcement for the paper "Concentration of random polytopes around the expected convex hull" by Daniel J. Fresen and Richard A. Vitale. Abstract: 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. Archive classification: math.PR math.FA Mathematics Subject Classification: 60D05, 60F99, 52A20, 52A22, 52B11 Remarks: 8 pages Submitted from: daniel.fresen@yale.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.2718 or http://arXiv.org/abs/1402.2718