Convex hulls of samples from spherically symmetric distributions (Q1175782)

The asymptotic behavior of the expected number of vertices, number of facets, probability content, surface area and volume of the convex hull of \(n\) independent random points in \(\mathbb{R}^d\) is determined as \(n\to\infty\). The random points are sampled from spherically symmetric distributions with so called algebraic, exponential or truncated tails. Well known special cases are the \(d\)-dimensional normal distribution and the uniform distribution in a \(d\)-ball. The estimates proved in the present article extend to higher dimensions results of \textit{H. Carnal}, who investigated the planar case [Z. Wahrscheinlichkeitstheorie Verw. Geb. 15, 168--178 (1970; Zbl 0193.46602)]. The author demonstrates that his results are useful for average case analysis of convex hull algorithms.