Optimal Transportation and Applications

Anisotropic transport-information inequalities

speaker: Jan Maas (IST Austria)

abstract: We prove upper bounds on the $L^\infty$-Wasserstein distance 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 generalise a recent result by Calvez, Poyato, and Santambrogio on the rate of convergence in Fisher’s infinitesimal model from dimension 1 to arbitrary dimensions. This is joint work with Ksenia Khudiakova (ISTA) and Francesco Pedrotti (ISTA).

timetable:
Wed 4 Dec, 12:00 - 12:45, Aula Dini
<< Go back