A Proof of the Central Limit Theorem Using the 2-Wasserstein Metric

2024/02/26 by Chin, Calvin Wooyoung
#60F05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2402.17085

Abstract

We prove the Lindeberg--Feller central limit theorem without using characteristic functions or Taylor expansions, but instead by measuring how far a distribution is from the standard normal distribution according to the 2-Wasserstein metric. This falls under the category of renormalization group methods. The facts we need about the metric are explained and proved in detail. We illustrate the idea on a classical version of the central limit theorem before going into the main proof.

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