Connes distance and optimal transport
Mathematical Physics
2018-03-28 v1 math.MP
Operator Algebras
Abstract
We give a brief overview on the relation between Connes spectral distance in noncommutative geometry and the Wasserstein distance of order 1 in optimal transport. We first recall how these two distances coincide on the space of probability measures on a Riemannian manifold. Then we work out a simple example on a discrete space, showing that the spectral distance between arbitrary states does not coincide with the Wasserstein distance with cost the spectral distance between pure states.
Cite
@article{arxiv.1803.07538,
title = {Connes distance and optimal transport},
author = {Pierre Martinetti},
journal= {arXiv preprint arXiv:1803.07538},
year = {2018}
}
Comments
Proceedings of the conference "Non-regular spacetime geometry", hold in Firenze, Italy, on 20-22 June 2017