# A dimension-free reverse logarithmic Sobolev inequality for low-complexity functions in Gaussian space

## TL;DR

This paper introduces a new, dimension-free reverse logarithmic Sobolev inequality for low-complexity functions in Gaussian space, improving upon previous results and providing novel proofs and formulations.

## Contribution

It presents a dimension-free version of the reverse logarithmic Sobolev inequality for low-complexity functions, enhancing prior work by Eldan (2018) with new proofs and forms.

## Key findings

- Dimension-free inequality established
- Improved bounds for low-complexity functions in Gaussian space
- New proofs and formulations provided

## Abstract

We discuss new proofs, and new forms, of a reverse logarithmic Sobolev inequality, with respect to the standard Gaussian measure, for low complexity functions, measured in terms of Gaussian-width. In particular, we provide a dimension-free improvement for a related result given in [Eldan '18].