Quantitative bounds for high dimensional entropic CLT

Chang-song Deng; Lin Wang; Lihu Xu

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arXiv · 2604.05861

Quantitative bounds for high dimensional entropic CLT

Chang-song Deng·Lin Wang·Lihu Xu

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Abstract

By extending the Johnson--Barron projection method from one dimension to high dimensions and utilizing a Wang type dimension-free Harnack inequality, we obtain a new quantitative bound for the entropic central limit theorem under the assumption that the Poincar\'e inequality holds. We compare our results with recent developments to demonstrate the merits of our approach.

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Chang-song Deng, Lin Wang, Lihu Xu. 2026-04-07. Quantitative bounds for high dimensional entropic CLT. https://arxiv.org/abs/2604.05861

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