Calculus of Variations and Geometric Measure Theory

L. Tamanini

A generalization of Costa's Entropy Power Inequality

created by tamanini1 on 23 Dec 2020
modified on 08 Jun 2022


Published Paper

Inserted: 23 dec 2020
Last Updated: 8 jun 2022

Journal: IEEE Transactions on Information Theory
Year: 2020

ArXiv: 2012.12230 PDF


Aim of this short note is to study Shannon's entropy power along entropic interpolations, thus generalizing Costa's concavity theorem. We shall provide two proofs of independent interest: the former by $\Gamma$-calculus, hence applicable to more abstract frameworks; the latter with an explicit remainder term, reminiscent of 20, allowing us to characterize the case of equality.