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Concentration of the Intrinsic Volumes of a Convex Body

Authors :
Lotz, Martin
McCoy, Michael B.
Nourdin, Ivan
Peccati, Giovanni
Tropp, Joel A.
Publication Year :
2018
Publisher :
arXiv, 2018.

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.<br />Comment: 18 pages. v4 with minor revisions

Details

Database :
OpenAIRE
Accession number :
edsair.doi.dedup.....6f27471812df4db5dda3acd7fd0fd52e
Full Text :
https://doi.org/10.48550/arxiv.1810.12412