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math.PR2026
A very short proof of the subgaussian convex-order comparison theorem
Antoine Song, Michel Talagrand
We provide a very short proof of the following comparison theorem, which has recently played an important role: every centered subgaussian random vector is dominated in convex orde…
math.PR2026
On Talagrand's Convexity Conjecture
Dongming Merrick Hua, Antoine Song, Stefan Tudose
We prove that any random vector in which is dominated in convex order by a standard Gaussian vector can be written as the sum of three standard Gaussian vectors. Thi…