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Journal Articles SIAM Journal on Discrete Mathematics Year : 2012

A curved Brunn-Minkowski inequality on the discrete hypercube

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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.

Dates and versions

inria-00540479 , version 1 (04-09-2013)

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Yann Ollivier, Cédric Villani. A curved Brunn-Minkowski inequality on the discrete hypercube. SIAM Journal on Discrete Mathematics, 2012, 26 (3), pp.983-996. ⟨10.1137/11085966X⟩. ⟨inria-00540479⟩
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