On mean outer radii of random polytopes David Alonso-GutierrezNikos DafnisMaria A. Hernandez-CifreJoscha Prochno Primary 52A22Secondary 52A2305D40Mean outer radiirandom polytopeisotropic constant In this paper, we introduce a new sequence of quantities for random polytopes. Let $K_N=\conv{X_1,\dots,X_N\}$ be a random polytope generated by independent random vectors uniformly distributed in an isotropic convex body $K$ of $\mathbb{R}^n$. We prove that the so-called $k$-th mean outer radius $\tilde{R}_k(K_N)$ has order $\max\{\sqrt{k},\sqrt{\log N}\}L_K$ with high probability if $n^2\leq N\leq e^{\sqrt{n}}$. We also show that this is the right order of the expected value of $\tilde{R}_k(K_N)$ in the full range $n\leq N\leq e^{\sqrt{n}}$. Indiana University Mathematics Journal 2014 text pdf 10.1512/iumj.2014.63.5231 10.1512/iumj.2014.63.5231 en Indiana Univ. Math. J. 63 (2014) 579 - 595 state-of-the-art mathematics http://iumj.org/access/