McKean's Conjecture Under the Log-Concavity Assumption

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...

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Bibliographic Details
Main Author: Geng, Yanlin
Format: Conference Proceeding
Language:English
Subjects:
Entropy
Heating systems
Information theory
Linear matrix inequalities
Random variables
Online Access:Request full text
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Summary: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 .
ISSN:2157-8117
DOI:10.1109/ISIT57864.2024.10619650