Unimodality for Radon Partitions of Random Vectors
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 ) .
Authors
- Gil Kalai (ORCID: https://orcid.org/0000-0003-0982-1000)
- Bhargav Narayanan
- Moshe White
- Natalya Ter-Saakov
Institutions
- Rutgers, The State University of New Jersey (US)
- Reichman University (IL)
- Hebrew University of Jerusalem (IL)
Publication Details
- Journal
- Discrete & Computational Geometry
- Published
- 2026-09-07
- DOI
- https://doi.org/10.1007/s00454-026-00870-6
- Primary Topic
- Point processes and geometric inequalities
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Alfred P. Sloan Foundation
- Israel Science Foundation
- European Research Council
- Division of Mathematical Sciences