Equality cases in the Anantharam-Jog-Nair inequality
Efe Aras, Thomas A. Courtade, Albert Zhang
TL;DR
This paper resolves the open problems of extremizability and extremizer characterization in the unified inequality by Anantharam, Jog, and Nair, which combines the Shannon-Stam and Brascamp-Lieb inequalities.
Contribution
It provides a complete solution to the extremizability and extremizer characterization problems for the unified inequality.
Findings
Extremizers are fully characterized.
Conditions for extremizability are established.
The results unify and extend previous inequalities.
Abstract
Anantharam, Jog and Nair recently unified the Shannon-Stam inequality and the entropic form of the Brascamp-Lieb inequalities under a common inequality. They left open the problems of extremizability and characterization of extremizers. Both questions are resolved in the present paper.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Graph theory and applications · Mathematical Inequalities and Applications