We give a short overview on a recently developed notion of Ricci curvature for discrete spaces. This notion relies on geodesic convexity properties of the relative entropy along geodesics in the space of probability densities, for a metric which is similar to (but different from) the 2-Wasserstein metric. The theory can be considered as a discrete counterpart to the theory of Ricci curvature for geodesic measure spaces developed by Lott–Sturm–Villani.
CITATION STYLE
Maas, J. (2017). Entropic ricci curvature for discrete spaces. In Lecture Notes in Mathematics (Vol. 2184, pp. 159–174). Springer Verlag. https://doi.org/10.1007/978-3-319-58002-9_5
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