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The entropy power conjecture implies the McKean conjecture

Guillaume Wang

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.

The entropy power conjecture implies the McKean conjecture

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.
Paper Structure (2 theorems, 8 equations)

This paper contains 2 theorems, 8 equations.

Key Result

Proposition 1

For any $M \in \mathbb{N}$, if eq:entropy_power holds for all $m \leq M$, then eq:mckean holds for all $m \leq M$.

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Lemma 1
  • proof