Random points on the boundary of smooth convex bodies

The convex hull of n independent random points chosen on the boundary of a convex body K ⊂ Rᵈ according to a given density function is a random polytope. The expectation of its i–th intrinsic volume for i=1, , d is investigated. In the case that the boundary of K is sufficiently smooth, asymptotic expansions for these expected intrinsic volumes as n → ∞ are derived.