A curved Brunn-Minkowski inequality on the discrete hypercube

Yann Ollivier 1, 2, * Cédric Villani 3
* Auteur correspondant
2 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
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.
Type de document :
Article dans une revue
Siam Journal on Discrete Mathematics, Society for Industrial and Applied Mathematics, 2012, 26 (3), pp.983-996
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https://hal.inria.fr/inria-00540479
Contributeur : Yann Ollivier <>
Soumis le : mercredi 4 septembre 2013 - 14:10:14
Dernière modification le : jeudi 11 janvier 2018 - 06:24:29

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  • HAL Id : inria-00540479, version 1
  • ARXIV : 1011.4779

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Yann Ollivier, Cédric Villani. A curved Brunn-Minkowski inequality on the discrete hypercube. Siam Journal on Discrete Mathematics, Society for Industrial and Applied Mathematics, 2012, 26 (3), pp.983-996. 〈inria-00540479〉

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