[2605.10908] On Talagrand's Convexity Conjecture
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arXiv:2605.10908 (math)
[Submitted on 11 May 2026]
Title:On Talagrand's Convexity Conjecture
Authors:Dongming Merrick Hua, Antoine Song, Stefan Tudose<br>View a PDF of the paper titled On Talagrand's Convexity Conjecture, by Dongming Merrick Hua and 2 other authors
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Abstract: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.
Comments:<br>14 pages, no figures. Comments welcomed!
Subjects:
Probability (math.PR); Combinatorics (math.CO); Metric Geometry (math.MG)
Cite as:<br>arXiv:2605.10908 [math.PR]
(or<br>arXiv:2605.10908v1 [math.PR] for this version)
https://doi.org/10.48550/arXiv.2605.10908
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arXiv-issued DOI via DataCite
Submission history<br>From: Dongming Hua [view email]<br>[v1]<br>Mon, 11 May 2026 17:47:36 UTC (21 KB)
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