A reverse entropy power inequality for log-concave random vectors

TL;DR

This paper introduces a new inequality related to the entropy of projections of log-concave vectors, proposing a novel semi-norm and conjectures on reverse entropy power inequalities within this setting.

Contribution

It establishes that the entropy exponent of one-dimensional projections forms a 1/5-seminorm and presents conjectures on reverse entropy power inequalities for log-concave vectors.

Findings

Entropy exponent defines a 1/5-seminorm for projections

Proposes conjectures on reverse entropy power inequalities

Discusses examples of log-concave vectors

Abstract

We prove that the exponent of the entropy of one dimensional projections of a log-concave random vector defines a 1/5-seminorm. We make two conjectures concerning reverse entropy power inequalities in the log-concave setting and discuss some examples.