Forward and Reverse Entropy Power Inequalities in Convex Geometry

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 Rényi 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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Cite this paper

@article{Madiman2016ForwardAR, title={Forward and Reverse Entropy Power Inequalities in Convex Geometry}, author={Mokshay M. Madiman and James Melbourne and Peng Xu}, journal={CoRR}, year={2016}, volume={abs/1604.04225} }