1. Concentration of the Intrinsic Volumes of a Convex Body
- Author
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Lotz, Martin, McCoy, Michael B., Nourdin, Ivan, Peccati, Giovanni, and Tropp, Joel A.
- Subjects
Mathematics - Metric Geometry ,Computer Science - Information Theory ,Mathematics - Probability ,Primary: 52A39, 52A20. Secondary: 94A17, 52A22 - 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., Comment: 18 pages. v4 with minor revisions
- Published
- 2018