Quantitative bounds for high dimensional entropic CLT

TL;DR

This paper extends the Johnson--Barron projection method to high dimensions and uses a Wang type Harnack inequality to derive new quantitative bounds for the entropic CLT under Poincaré inequality assumptions.

Contribution

It introduces a high-dimensional extension of the Johnson--Barron projection method combined with a dimension-free Harnack inequality for entropic CLT bounds.

Findings

Derived a new quantitative bound for high-dimensional entropic CLT.

Extended the Johnson--Barron projection method to multiple dimensions.

Compared results with recent developments to highlight improvements.

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.