Lower bound for the coarse Ricci curvature of continuous-time pure jump processes

2017/05/18 by Villemonais, Denis
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1705.06642

Abstract

We obtain a lower bound for the coarse Ricci curvature of continuous time pure jump Markov processes, with an emphasis on interacting particle systems. Applications to several models are provided, with a detailed study of the herd behavior of a simple model of interacting agents.

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• Ricci curvature bounds for weakly interacting Markov chains
• Mixing and Concentration by Ricci Curvature
• Wasserstein decay of one dimensional jump-diffusions
• Ricci curvature and W₁-exponential convergence of Markov processes on graphs