Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order

Yihan Zhang

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arXiv · 2604.26819

Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order

Yihan Zhang

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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 $f$. This is sharp as witnessed by $ X \sim \mathrm{Unif}(\{-1,1\}) $ and $ f(x) = |x| $.

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Yihan Zhang. 2026-04-29. Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order. https://arxiv.org/abs/2604.26819

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