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In this paper we study the coarse Ricci curvature on the space of probabilitymeasures on a metric space. The infimum of the $p$-coarse Ricci curvature onthe $L^p$-Wasserstein space coincides with that with respect to the originalrandom walk. Considering a random walk as a map, we investigate the relationbetween Gromov-Hausdorff convergence and the $p$-coarse Ricci curvature. Wealso study the concentration of measure phenomenon related to the coarse Riccicurvature.

Coarse Ricci curvature on the space of probability measures