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Let $\Xi_n=\{\xi_1,\dots,\xi_n\}$ be a sample of $n$ independent pointsdistributed on a regular closed element $K$ of the extended convex ring in$\mathbb{R}^d$ according to a probability measure $\mu$ on $K$, admitting adensity function. We consider random sets generated from the intersection ofthe translations of $K$ by elements of $\Xi_n$, as $X_n=\bigcap_{i=1}^n(K-\xi_i)$. The aim of this work is to show that scaled $X_n$ as $n\to\infty$converges in distribution to the zero cell of a Poisson hyperplane tessellationwhose distributionis is determined by the curvature measure of $K$ and thebehaviour of the density of $\mu$ near the boundary of $K$.

Intersections of randomly translated sets