Coarse Ricci curvature for continuous-time Markov processes

Laurent Veysseire (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

The coarse Ricci curvature for Markov chains is generalized for continuous time. We show that a positive coarse Ricci curvature implies a contraction of the Markov process for the Wasserstein distance between probability measures. This leads to a spectral gap estimate in the reversible case.

Mots clés: coarse Ricci curvature; contraction of Wasserstein distance; spectral gap

Domaines: Probabilités [math.PR]

Laurent Veysseire. Coarse Ricci curvature for continuous-time Markov processes. 2012. ⟨hal-00665610⟩