# Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order

arXiv: https://arxiv.org/abs/2604.26819 · HTML: https://mlsanity.com/paper/2604.26819/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 8 references that are in the map.
- First posted on arXiv 29 Apr 2026.

## Builds on (most cited first, 1 of 1)

- [Large Deviation Methods for Approximate Probabilistic Inference](https://mlsanity.com/paper/1301.7392/) (2013)

## Abstract (arXiv)

We prove that any random variable X whose moment generating function is point-wise upper bounded by that of  G ~ N(0,1)  must be dominated by  G/mathbbE[|G|]  in convex order, meaning  mathbbE[f(X)] ≤ mathbbE[f(G/mathbbE[|G|])]  for all convex f. This is sharp as witnessed by  X ~ Unif(-1,1)  and  f(x) = |x| .