Concentration of the Intrinsic Volumes of a Convex Body

Martin Lotz, Michael B. McCoy, Ivan Nourdin, Giovanni Peccati, Joel A. Tropp

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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