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arXiv · 1301.0978

Coarse Ricci curvature on the space of probability measures

Yu Kitabeppu
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Abstract

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.

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Yu Kitabeppu. 2013-01-06. Coarse Ricci curvature on the space of probability measures. https://arxiv.org/abs/1301.0978

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