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Abstract: We compare two approaches to Ricci curvature on non-smooth spaces, in thecase of the discrete hypercube $\{0,1\}^N$. While the coarse Ricci curvature ofthe first author readily yields a positive value for curvature, thedisplacement convexity property of Lott, Sturm and the second author could notbe fully implemented. Yet along the way we get new results of a combinatorialand probabilistic nature, including a curved Brunn-Minkowski inequality on thediscrete hypercube.



Author: Yann Ollivier, C├ędric Villani

Source: https://arxiv.org/







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