@unpublished{17352,
  abstract     = {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 simplest setting, such a bound amounts to a
transport-information inequality involving the $L^\infty$-Wasserstein metric
and the relative $L^\infty$-Fisher information. We show that this inequality
can be sharpened significantly in situations where the involved densities are
anisotropic. Our proof is based on probabilistic techniques using Langevin
dynamics. As an application of these results, we obtain sharp exponential rates
of convergence in Fisher's infinitesimal model from quantitative genetics,
generalising recent results by Calvez, Poyato, and Santambrogio in dimension 1
to arbitrary dimensions.},
  author       = {Khudiakova, Kseniia and Maas, Jan and Pedrotti, Francesco},
  booktitle    = {arXiv},
  title        = {{L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher's infinitesimal model}},
  doi          = {10.48550/arXiv.2402.04151},
  year         = {2024},
}