On Talagrand's Convexity Conjecture
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866909033685843968 |
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| author | Hua, Dongming Merrick Song, Antoine Tudose, Stefan |
| author_facet | Hua, Dongming Merrick Song, Antoine Tudose, Stefan |
| contents | We prove that any centered $1$-subgaussian random vector in $\mathbb{R}^{n}$ can be written as the sum of a universal number of standard Gaussian vectors. Following the work of the second-named author, this solves M. Talagrand's convexity problem, which in turn implies a combinatorial analogue of the problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10908 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Talagrand's Convexity Conjecture Hua, Dongming Merrick Song, Antoine Tudose, Stefan Probability Combinatorics Metric Geometry We prove that any centered $1$-subgaussian random vector in $\mathbb{R}^{n}$ can be written as the sum of a universal number of standard Gaussian vectors. Following the work of the second-named author, this solves M. Talagrand's convexity problem, which in turn implies a combinatorial analogue of the problem. |
| title | On Talagrand's Convexity Conjecture |
| topic | Probability Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2605.10908 |