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New math paper proves sharp one-dimensional sub-Gaussian comparison in convex order

By PulseAugur Editorial · [2 sources] ·

Researchers have published a paper detailing a sharp one-dimensional sub-Gaussian comparison in convex order. The study proves that a random variable X, whose moment generating function is bounded by that of a standard normal distribution, is dominated by a scaled normal distribution in convex order. This mathematical finding has implications for understanding the properties of random variables and their distributions. AI

IMPACT Provides theoretical underpinnings for understanding random variable properties, potentially influencing future AI model robustness analysis.

RANK_REASON This is a research paper published on arXiv concerning mathematical probability and statistics.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New math paper proves sharp one-dimensional sub-Gaussian comparison in convex order

COVERAGE [2]

  1. arXiv stat.ML TIER_1 English(EN) · Yihan Zhang ·

    Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order

    arXiv:2604.26819v1 Announce Type: cross 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 \…

  2. arXiv stat.ML TIER_1 English(EN) · Yihan Zhang ·

    Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order

    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 $…

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