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math.PR2024
Stochastic proof of the sharp symmetrized Talagrand inequality
Thomas A. Courtade, Max Fathi, Dan Mikulincer
We give a new proof of the sharp symmetrized form of Talagrand's transport-entropy inequality. Compared to stochastic proofs of other Gaussian functional inequalities, the new idea…
math.PR2023
HWI inequalities in discrete spaces via couplings
Thomas A. Courtade, Max Fathi
HWI inequalities are interpolation inequalities relating entropy, Fisher information and optimal transport distances. We adapt an argument of Y. Wu for proving the Gaussian HWI ine…