A friendly proof of the Berry-Esseen theorem
Probability
2026-02-09 v1
Abstract
A gem of classical probability, the Berry-Esseen theorem provides a non-asymptotic form of the central limit theorem. This note gives a friendly and intuitive exposition of the classical Fourier-analytic proof of Esseen's smoothing inequality and, as a consequence, a general Berry-Esseen theorem for non-i.i.d random variables. The exposition is suitable for use in a basic graduate course in probability.
Keywords
Cite
@article{arxiv.2602.06234,
title = {A friendly proof of the Berry-Esseen theorem},
author = {Roman Vershynin},
journal= {arXiv preprint arXiv:2602.06234},
year = {2026}
}
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9 pages