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arXiv · 2512.18588

On the subgaussian comparison theorem

Ramon van Handel
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Abstract

The aim of this expository note is to prove that any $1$-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.

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Ramon van Handel. 2025-12-21. On the subgaussian comparison theorem. https://arxiv.org/abs/2512.18588

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