Covering numbers and ``low M^*-estimate'' for quasi-convex bodies

1996/05/20 by Alexander E. Litvak, A. E. Litvak, Vitali Milman +6
Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.FA #math.MG

paper · pdf · doi:10.48550/arxiv.math/9605223

arxiv created 1996/05/20 · openalex publication_date 1996/05/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article gives estimates on covering numbers and diameters of random proportional sections and projections of symmetric quasi-convex bodies in \mathbb R. These results were known for the convex case and played an essential role in development of the theory. Because duality relations can not be applied in the quasi-convex setting, new ingredients were introduced that give new understanding for the convex case as well.

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