Random convex hulls in a product of balls (Q1826119)

The convex hull of a set of points sampled independently and uniformly from the Cartesian product of balls of various dimensions is investigated. Bounds on the asymptotic behavior of the expected combinatorial complexity, volume, and mean width are derived when the distribution is held fixed and the sample size approaches infinity. The expected combinatorial complexity and volume are found to depend (up to constant factors) only on the greatest dimension of any factor ball and the number of balls of that dimension. On the other hand, the expected mean width depends only on the number of balls and the dimension of the product.