$L^{\infty }$-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher's infinitesimal model

Ksenia A. Khudiakova, Jan Maas, Francesco Pedrotti

We prove upper bounds on the $L^{\infty }$-Wasserstein distance from optimal transport between strongly log-concave probability densities and log-Lipschitz perturbations. In the simpl…