Functional inequalities along Wasserstein geodesics

Nathael Gozlan, Hugo Malamut, Irène Waldspurger

We study functional inequalities along Wasserstein geodesics. If $\mu$ 0 and $\mu$ 1 are respectively $\kappa$ 0 -and $\kappa$ 1 -strongly log-concave probability measures on R n , we prove that…