Forward and Reverse Entropy Power Inequalities in Convex Geometry
Information Theory
2020-02-07 v2 Functional Analysis
math.IT
Probability
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
Keywords
Cite
@article{arxiv.1604.04225,
title = {Forward and Reverse Entropy Power Inequalities in Convex Geometry},
author = {Mokshay Madiman and James Melbourne and Peng Xu},
journal= {arXiv preprint arXiv:1604.04225},
year = {2020}
}
Comments
54 pages. Changes in v2: improved organization, cleaned up exposition, and numerous references added