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New Connections Between the Entropy Power Inequality and Geometric Inequalities

Marsiglietti, Arnaud and Kostina, Victoria (2018) New Connections Between the Entropy Power Inequality and Geometric Inequalities. In: 2018 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 1978-1982. ISBN 978-1-5386-4780-6. https://resolver.caltech.edu/CaltechAUTHORS:20181126-145018270

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Abstract

The entropy power inequality (EPI) has a fundamental role in Information Theory, and has deep connections with famous geometric inequalities. In particular, it is often compared to the Brunn-Minkowski inequality in convex geometry. In this article, we further strengthen the relationships between the EPI and geometric inequalities. Specifically, we establish an equivalence between a strong form of reverse EPI and the hyperplane conjecture, which is a long-standing conjecture in high-dimensional convex geometry. We also provide a simple proof of the hyperplane conjecture for a certain class of distributions, as a straightforward consequence of the EPI.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ISIT.2018.8437604DOIArticle
ORCID:
AuthorORCID
Marsiglietti, Arnaud0000-0002-7459-0547
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2018 IEEE. Supported by the Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship. Supported in part by the National Science Foundation (NSF) under Grant CCF-1566567.
Funders:
Funding AgencyGrant Number
Center for the Mathematics of Information, CaltechUNSPECIFIED
NSFCCF-1566567
Subject Keywords:Entropy power inequality, reverse entropy power inequality, hyperplane conjecture
Record Number:CaltechAUTHORS:20181126-145018270
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181126-145018270
Official Citation:A. Marsiglietti and V. Kostina, "New Connections Between the Entropy Power Inequality and Geometric Inequalities," 2018 IEEE International Symposium on Information Theory (ISIT), Vail, CO, 2018, pp. 1978-1982. doi: 10.1109/ISIT.2018.8437604
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91190
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Nov 2018 23:07
Last Modified:03 Oct 2019 20:32

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