A Proof of the Central Limit Theorem Using the $2$-Wasserstein Metric
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929257780871168 |
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| author | Chin, Calvin Wooyoung |
| author_facet | Chin, Calvin Wooyoung |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Proof of the Central Limit Theorem Using the $2$-Wasserstein Metric Chin, Calvin Wooyoung Probability 60F05 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. |
| title | A Proof of the Central Limit Theorem Using the $2$-Wasserstein Metric |
| topic | Probability 60F05 |
| url | https://arxiv.org/abs/2402.17085 |