Coarse Ricci curvature for continuous-time Markov processes

2012/02/02 by Laurent Veysseire, Veysseire, Laurent · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1202.0420

openalex publication_date 2012/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians
• A concentration theorem for the equilibrium measure of Markov chains with nonnegative coarse Ricci curvature

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