A proof of the central limit theorem using the $2$-Wasserstein metric
Year: 2025
Type: article
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.
Source: L’Enseignement Mathématique
DOI: 10.4171/lem/1094
Author: Calvin Wooyoung Chin
Institution: Apple (United States)
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4407528916