An application of the probabilistic method to Tverberg's theorem.
Pablo Soberón · Open Collections · 2017
We show how the probabilistic method can be applied to obtain robust versions of this Tverberg's theorem. In particular, given positive integers $r, d, t$, we study the number of points needed in $\mathbb{R}^d$ to guarantee the existence of a partition of them into r parts such that, even after any t points are removed, the convex hulls of what is left in each part have non-empty intersection.