Beyond the entropy power inequality, via rearrangements
Information Theory
2015-05-07 v2 Functional Analysis
math.IT
Probability
Abstract
A lower bound on the R\'enyi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements. For the special case of Boltzmann-Shannon entropy, this lower bound is better than that given by the entropy power inequality. Several applications are discussed, including a new proof of the classical entropy power inequality and an entropy inequality involving symmetrization of L\'evy processes.
Keywords
Cite
@article{arxiv.1307.6018,
title = {Beyond the entropy power inequality, via rearrangements},
author = {Liyao Wang and Mokshay Madiman},
journal= {arXiv preprint arXiv:1307.6018},
year = {2015}
}
Comments
32 pages. v2: Several minor edits + Section X added