Gaussian marginals of convex bodies with symmetries

TL;DR

This paper establishes Gaussian approximation theorems for certain low-dimensional marginals of symmetric convex bodies, including those with 1-unconditional bases and simplices, extending previous one-dimensional results.

Contribution

It introduces new Gaussian approximation results for specific marginals of convex bodies with symmetries, broadening the scope of prior work.

Findings

Gaussian approximation theorems for k-dimensional marginals

Extension of previous 1-dimensional marginal results

Applicable to bodies with 1-unconditional bases and simplices

Abstract

We prove Gaussian approximation theorems for specific $k$-dimensional marginals of convex bodies which possess certain symmetries. In particular, we treat bodies which possess a 1-unconditional basis, as well as simplices. Our results extend recent results for 1-dimensional marginals due to E. Meckes and the author.