  In this paper we study the coarse Ricci curvature on the space of probability
measures on a metric space. The infimum of the $p$-coarse Ricci curvature on
the $L^p$-Wasserstein space coincides with that with respect to the original
random walk. Considering a random walk as a map, we investigate the relation
between Gromov-Hausdorff convergence and the $p$-coarse Ricci curvature. We
also study the concentration of measure phenomenon related to the coarse Ricci
curvature.
