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 two different proofs of the Berry-Esseen theorem for nonidentically distributed random variables: the classical Fourier-analytic proof and a proof by Stein's method following E. Bolthausen. Both proofs are self-contained; the reader may read either proof without reading the other. The exposition is suitable for a basic graduate course in probability.
From: Roman Vershynin [view email]
[v1]
Thu, 5 Feb 2026 22:22:34 UTC (10 KB)
[v2]
Thu, 30 Jul 2026 16:29:03 UTC (15 KB)
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