Concentration of the Intrinsic Volumes of a Convex Body

2018/10/29 by Lotz, Martin, McCoy, Michael B., Nourdin, Ivan +2 · 2 citations
#52A20. Secondary: 94A17 #52A22 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Metric Geometry (math.MG) #Primary: 52A39 #Probability (math.PR)

paper · doi:10.48550/arxiv.1810.12412

Abstract

The intrinsic volumes are measures of the content of a convex body. This paper uses probabilistic and information-theoretic methods to study the sequence of intrinsic volumes of a convex body. The main result states that the intrinsic volume sequence concentrates sharply around a specific index, called the central intrinsic volume. Furthermore, among all convex bodies whose central intrinsic volume is fixed, an appropriately scaled cube has the intrinsic volume sequence with maximum entropy.

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• Approximation of the Euclidean ball by polytopes with a fixed number of k-faces
• On Convex Functions of Gaussian Variables

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