Concentration of the Intrinsic Volumes of a Convex Body

10/29/2018

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by   Martin Lotz, et al.

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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.