Convex subsets of non-convex Lorentz balls

Abstract

Many star bodies have convex subsets with approximately the same Gaussian measure (of the complement). Inspired by this phenomenon, and in connection with the randomized Dvoretzky theorem for Lorentz spaces, we derive bounds on the distribution of certain functions of a Gaussian random vector by approximating their sub-level sets by convex subsets.

18 pages. Most of the material here was originally part of arXiv:2104.11974 and now stands as a paper on its own