Random polytopes in the d-dimensional cube (Q1085440)

Let A(n) denote a random n-element subset of the vertices of the d- dimensional cube \([-1,1]^ d\). The author shows that, for any \(c\in {\mathbb{R}}\), \(\Pr ob (0\in\) convex hull of \(A(2d+c\sqrt{2d}))=\Phi (c),\) where \(\Phi\) (c) is the normal distribution function. This theorem is a particular consequence of results obtained by Winder and Cover [cf. \textit{R. O. Winder}, SIAM J. Appl. Math. 14, 811-818 (1966; Zbl 0161.136), and the references cited there]. The reviewer could not find out where the author used the ''inductional method'' mentioned in section 4.