On the subgaussian comparison theorem
Probability
2025-12-23 v1
Abstract
The aim of this expository note is to prove that any -subgaussian random vector is dominated in the convex ordering by a universal constant times a standard Gaussian vector. This strengthens Talagrand's celebrated subgaussian comparison theorem. The proof combines a tensorization argument due to J. Liu with ideas that date back to the work of Fernique.
Cite
@article{arxiv.2512.18588,
title = {On the subgaussian comparison theorem},
author = {Ramon van Handel},
journal= {arXiv preprint arXiv:2512.18588},
year = {2025}
}
Comments
8 pages