Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order

• URL: http://arxiv.org/abs/2604.26819v1
• Date: Wed, 29 Apr 2026 15:47:30 GMT
• Title: Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order
• Abstract summary: Equality is attained by taking $ X sim mathrmUnif(-1,1) $ and $ f(x) = |x| $.
• Score: 7.802456101518216
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We prove that any random variable $X$ whose moment generating function is point-wise upper bounded by that of $ G \sim \mathcal{N}(0,1) $ must be dominated by $ G/\mathbb{E}[|G|] $ in convex order, meaning $ \mathbb{E}[f(X)] \le \mathbb{E}[f(G/\mathbb{E}[|G|])] $ for all convex $f$. Equality is attained by taking $ X \sim \mathrm{Unif}(\{-1,1\}) $ and $ f(x) = |x| $.

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