Theoretical analysis demonstrates strong unimodality for Radon partition size distributions in random Gaussian vectors, highlighting fundamental structural regularity in stochastic geometry.
Consider the (almost surely) unique Radon partition of a set of n random Gaussian vectors in Rⁿ⁻² R n - 2 ; choose one of the two parts of this partition uniformly at random, and for 0 ≤ k ≤ n 0 ≤ k ≤ n , let pₖ p k denote the probability that it has size k k . In this paper, we prove strong unimodality results for the distribution (p₀, ,pₙ) ( p 0 , ⋯ , p n ) .
No takes yet. Share an insight, caveat, or question.
Kalai et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: