This note presents a sharp transport-entropy inequality that improves on Talagrand’s inequality for the Gaussian measure, arising as a dual formulation of the functional Santaló inequality. We also discuss some extensions and connections with concentration of measure.
"A sharp symmetrized form of Talagrand’s transport-entropy inequality for the Gaussian measure." Electron. Commun. Probab. 23 1 - 9, 2018. https://doi.org/10.1214/18-ECP179