Unimodality for Radon Partitions of Random Vectors

Abstract

Abstract Consider the (almost surely) unique Radon partition of a set of n random Gaussian vectors in $$\mathbb {R}^{n-2}$$ R n - 2 ; choose one of the two parts of this partition uniformly at random, and for $$0 \le k \le n$$ 0 ≤ k ≤ n , let $$ p_k $$ p k denote the probability that it has size $$ k $$ k . In this paper, we prove strong unimodality results for the distribution $$(p_0,\dots ,p_n)$$ ( p 0 , ⋯ , p n ) .