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

Ivan Gentil (1)

1 ICJ - Institut Camille Jordan

We prove a refined contraction inequality for diffusion semigroups with respect to the Wasserstein distance on a 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. The theorem is proved by using a dimensional coercive estimate for the Hodge-de Rham semigroup on 1-forms.

Mots clés: Diffusion equations; Wasserstein distance; 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. 2013. ⟨hal-00873097v1⟩