Unimodality for Radon partitions of random vectors
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911033729220608 |
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| author | Chan, Swee Hong Kalai, Gil Narayanan, Bhargav Ter-Saakov, Natalya White, Moshe |
| author_facet | Chan, Swee Hong Kalai, Gil Narayanan, Bhargav Ter-Saakov, Natalya White, Moshe |
| contents | 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 $(p_0,\dots,p_n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01353 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unimodality for Radon partitions of random vectors Chan, Swee Hong Kalai, Gil Narayanan, Bhargav Ter-Saakov, Natalya White, Moshe Combinatorics Probability 05A20, 52A35 (Primary) 52A40, 60C05, 60F05, 62G30 (Secondary) 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 $(p_0,\dots,p_n)$. |
| title | Unimodality for Radon partitions of random vectors |
| topic | Combinatorics Probability 05A20, 52A35 (Primary) 52A40, 60C05, 60F05, 62G30 (Secondary) |
| url | https://arxiv.org/abs/2507.01353 |