2000 character limit reached
Forward and Reverse Entropy Power Inequalities in Convex Geometry (1604.04225v2)
Published 14 Apr 2016 in cs.IT, math.FA, math.IT, and math.PR
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