Forward and Reverse Entropy Power Inequalities in Convex Geometry

  • Madiman M
  • Melbourne J
  • Xu P
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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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Madiman, M., Melbourne, J., & Xu, P. (2017). Forward and Reverse Entropy Power Inequalities in Convex Geometry (pp. 427–485). https://doi.org/10.1007/978-1-4939-7005-6_14

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