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arXiv · 1810.12412

Concentration of the Intrinsic Volumes of a Convex Body

Martin Lotz·Michael B. McCoy·Ivan Nourdin·Giovanni Peccati·Joel A. Tropp
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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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Martin Lotz, Michael B. McCoy, Ivan Nourdin, Giovanni Peccati, Joel A. Tropp. 2018-10-29. Concentration of the Intrinsic Volumes of a Convex Body. https://arxiv.org/abs/1810.12412

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