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arXiv · 2507.01353

Unimodality for Radon partitions of random vectors

Swee Hong Chan·Gil Kalai·Bhargav Narayanan·Natalya Ter-Saakov·Moshe White
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Abstract

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

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Swee Hong Chan, Gil Kalai, Bhargav Narayanan, Natalya Ter-Saakov, Moshe White. 2025-07-02. Unimodality for Radon partitions of random vectors. https://arxiv.org/abs/2507.01353

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