{"ID":6193384,"CreatedAt":"2026-07-09T09:46:01.859313918Z","UpdatedAt":"2026-07-09T12:56:29.822227725Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2605.10908","arxiv_id":"2605.10908","title":"On Talagrand's Convexity Conjecture","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.","short_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.","url_abs":"https://arxiv.org/abs/2605.10908","url_pdf":"https://arxiv.org/pdf/2605.10908v1","authors":"[\"Dongming Merrick Hua\",\"Antoine Song\",\"Stefan Tudose\"]","published":"2026-05-11T17:47:36Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.CO\",\"math.MG\"]","methods":"[]","has_code":false}