A View on Optimal Transport from Noncommutative Geometry

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2010
• Main Authors: D'Andrea, F., Martinetti, P.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146358
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A View on Optimal Transport from Noncommutative Geometry / F. D'Andrea, P. Martinetti // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 44 назв. — англ.

We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry. Starting from a remark of Rieffel on compact manifolds, we first...