Gaussian marginals of convex bodies with symmetries

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.

v4: major revision incorporating recent improvements in the main technical tools. To appear in Beitraege Algebra Geom