Forward and Reverse Entropy Power Inequalities in Convex Geometry

Mokshay Madiman; James Melbourne; Peng Xu

doi:10.1007/978-1-4939-7005-6_14

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arXiv · 1604.04225

Forward and Reverse Entropy Power Inequalities in Convex Geometry

Mokshay Madiman·James Melbourne·Peng Xu

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Abstract

The entropy power inequality, which plays a fundamental role in information theory and probability, may be seen as an analogue of the Brunn-Minkowski inequality. Motivated by this connection to Convex Geometry, we survey various recent developments on forward and reverse entropy power inequalities not just for the Shannon-Boltzmann entropy but also more generally for R\'enyi entropy. In the process, we discuss connections between the so-called functional (or integral) and probabilistic (or entropic) analogues of some classical inequalities in geometric functional analysis

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Mokshay Madiman, James Melbourne, Peng Xu. 2016-04-14. Forward and Reverse Entropy Power Inequalities in Convex Geometry. https://doi.org/10.1007/978-1-4939-7005-6_14

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