Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold

Ivan Gentil (1)

1 EDPA - Équations aux dérivées partielles, analyse

We prove a refined contraction inequality for diffusion semigroups with respect to the Wasserstein distance on a compact Riemannian manifold taking account of the dimension. The result generalizes in a Riemannian context, the dimensional contraction established in [BGG13] for the Euclidean heat equation. It is proved by using a dimensional coercive estimate for the Hodge-de Rham semigroup on 1-forms.

Mots clés: Wasserstein distance; Diffusion equations; Hodge-de Rham operator; Curvature-dimension bounds

Domaines: Probabilités [math.PR]

Ivan Gentil. Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold. Potential Analysis, 2015, 52 (4), pp.861-873. ⟨hal-00873097v3⟩