Convex subsets of non-convex Lorentz balls

2022/06/21 by Daniel J. Fresen, Fresen, Daniel J.
Mathematics · #52A27 #52A30 #60E05 #60E15 #FOS: Mathematics #Functional Analysis (math.FA) #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2206.10496

openalex publication_date 2022/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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