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Melbourne, J., Tkocz, T. and Wyczesany, K. orcid.org/0000-0002-1530-7916 (2025) A Rényi entropy interpretation of anti-concentration and noncentral sections of convex bodies. Communications in Contemporary Mathematics. ISSN 0219-1997
Abstract
We extend Bobkov and Chistyakov’s [Entropy power inequality for the Rényi entropy, IEEE Trans. Inform. Theory61(2) (2015) 708–714] upper bounds on concentration functions of sums of independent random variables to a multivariate entropic setting. The approach is based on pointwise estimates on densities of sums of independent random vectors uniform on centered Euclidean balls. In this vein, we also obtain sharp bounds on volumes of noncentral sections of isotropic convex bodies.
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Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This item is protected by copyright. This is an author produced version of an article published in Communications in Contemporary Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Concentration function, Sums of independent random variables, Rényi entropy, Anti-concentration, Sections of convex bodies, Pointwise lower bounds on convolutions |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 19 May 2025 08:42 |
Last Modified: | 19 May 2025 08:42 |
Published Version: | https://www.worldscientific.com/doi/pdf/10.1142/S0... |
Status: | Published online |
Publisher: | World Scientific Publishing |
Identification Number: | 10.1142/s0219199725500336 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:226705 |
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A Rényi entropy interpretation of anti-concentration and noncentral sections of convex bodies. (deposited 19 May 2025 08:17)
- A Rényi entropy interpretation of anti-concentration and noncentral sections of convex bodies. (deposited 19 May 2025 08:42) [Currently Displayed]
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