The entropy power conjecture implies the McKean conjecture

TL;DR

This paper demonstrates that the entropy power conjecture implies the McKean conjecture across all derivatives, using an elementary proof based on Bell polynomial manipulations.

Contribution

It establishes a novel implication between the entropy power and McKean conjectures, providing an elementary proof applicable to all derivative orders.

Findings

Entropy power conjecture implies McKean conjecture for all derivatives.

Elementary proof based on Bell polynomial manipulation.

Clarifies the relationship between these conjectures in information theory and probability.

Abstract

After reviewing the entropy power, the McKean, and the Gaussian completely monotone conjectures, we prove that the first implies the second, for each order of the time-derivative. The proof is elementary and is based on manipulating the Bell polynomials.