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McKean's Conjecture Under the Log-Concavity Assumption | IEEE Conference Publication | IEEE Xplore

McKean's Conjecture Under the Log-Concavity Assumption


Abstract:

McKean conjectured that Gaussian random variables are optimal for the n\text{th} order derivative of differential entropy along the heat flow, and verified this for $n=...Show More

Abstract:

McKean conjectured that Gaussian random variables are optimal for the n\text{th} order derivative of differential entropy along the heat flow, and verified this for n=1,2. Recently, Zhang, Anantharam and Geng introduced the linear matrix inequality approach to show that this conjecture holds for n \leq 5 under the log-concavity assumption. In this work, with the same assumption, we improve their method using the positive semidefinite reformulation and validate McKean's conjecture for n \leq 9, and also the completely monotone conjecture for n\leq 11.
Date of Conference: 07-12 July 2024
Date Added to IEEE Xplore: 19 August 2024
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Conference Location: Athens, Greece

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