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arXiv · 1011.4779

A curved Brunn--Minkowski inequality on the discrete hypercube

Yann Ollivier·Cédric Villani
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Abstract

We compare two approaches to Ricci curvature on non-smooth spaces, in the case of the discrete hypercube $\{0,1\}^N$. While the coarse Ricci curvature of the first author readily yields a positive value for curvature, the displacement convexity property of Lott, Sturm and the second author could not be fully implemented. Yet along the way we get new results of a combinatorial and probabilistic nature, including a curved Brunn--Minkowski inequality on the discrete hypercube.

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Yann Ollivier, Cédric Villani. 2010-11-22. A curved Brunn--Minkowski inequality on the discrete hypercube. https://arxiv.org/abs/1011.4779

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