Variance asymptotics for random polytopes in smooth convex bodies

Pierre Calka, J. E. Yukich

Let $K\subset {\mathbb{R}}^d$ be a smooth convex set and let $¶_\la$ be a Poisson point process on ${\mathbb{R}}^d$ of intensity $\la$. The convex hull of $¶_\la \cap K$ is a random convex polytope $…