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Concentration of the intrinsic volumes of a convex body
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Lotz, Martin, McCoy, Michael B., Nourdin, Ivan, Peccati, Giovanni and Tropp, Joel A. (2020) Concentration of the intrinsic volumes of a convex body. In: Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, 2266 . Cham: Springer, pp. 139-167. ISBN 9783030467616
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Official URL: https://doi.org/10.1007/978-3-030-46762-3_6
Abstract
The intrinsic volumes are measures of the content of a convex body. This paper applies probabilistic and information-theoretic methods to study the sequence of intrinsic volumes. 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.
| Item Type: | Book Item | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Convex domains , Convex geometry, Functional analysis , Curvature | ||||||||||||
| Series Name: | Lecture Notes in Mathematics | ||||||||||||
| Publisher: | Springer | ||||||||||||
| Place of Publication: | Cham | ||||||||||||
| ISBN: | 9783030467616 | ||||||||||||
| Book Title: | Geometric Aspects of Functional Analysis | ||||||||||||
| Official Date: | 9 July 2020 | ||||||||||||
| Dates: |
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| Volume: | 2266 | ||||||||||||
| Page Range: | pp. 139-167 | ||||||||||||
| DOI: | 10.1007/978-3-030-46762-3_6 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| Copyright Holders: | © Springer Nature Switzerland AG 2020 | ||||||||||||
| Date of first compliant deposit: | 30 January 2019 | ||||||||||||
| Date of first compliant Open Access: | 9 July 2021 | ||||||||||||
| RIOXX Funder/Project Grant: |
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