Convex geometry and point set configurations form a pivotal area of research in computational geometry, where the primary focus is the study of convex sets and the intricate arrangements of points in ...

We show that the random point measures induced by vertices in the convex hull of a Poisson sample on the unit ball, when properly scaled and centered, converge to those of a mean zero Gaussian field.

Let An, n≥ 1, be i.i.d. random closed sets in Rd. Limit theorems for their normalized convex hulls an -1 conv(A1∪ ⋯ ∪ An) are proved. The limiting distributions correspond to C-stable random sets. The ...