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 ) .
Fields of Study & Subjects
Point processes and geometric inequalities
Geometry and complex manifolds
Financial Risk and Volatility Modeling
Publication details
- Journal / source
- Discrete & Computational Geometry
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 7 September 2026
- Language
- EN