Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the infimum of the best constant in a functional inequality, the Brascamp-Lieb-like inequality, over auxiliary measures within a neighborhood of a product distribution. In the finite alphabet and the Gaussian cases, such an infimum converges to the best constant in a mutual information inequality. Implications for strong converse properties of two common randomness (CR) generation problems are discussed. In particular,  prove the strong converse property of the rate region for the omniscient helper CR generation problem in the discrete and the Gaussian cases. The latter case is a rare instance of a strong converse for a continuous source when the rate region involves auxiliary random variables.
['Jingbo Liu', 'Thomas A. Courtade', 'Paul Cuff', 'Sergio Verdu']
I am writing a research paper on a idea Smoothing Brascamp-Lieb inequalities and strong converses for common randomness generation
[{"from": "human", "value": "I am writing a research paper on a idea Smoothing Brascamp-Lieb inequalities and strong converses for common randomness generation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the infimum of the best constant in a functional inequality, the Brascamp-Lieb-like inequality, over auxiliary measures within a neighborhood of a product distribution. In the finite alphabet and the Gaussian cases, such an infimum converges to the best constant in a mutual information inequality. Implications for strong converse properties of two common randomness (CR) generation problems are discussed. In particular,  prove the strong converse property of the rate region for the omniscient helper CR generation problem in the discrete and the Gaussian cases. The latter case is a rare instance of a strong converse for a continuous source when the rate region involves auxiliary random variables."}]