Gromov-Hausdorff convergence of discrete transportation metrics

N. Gigli, J. Maas, SIAM Journal on Mathematical Analysis 45 (2013) 879–899.


Journal Article | Published
Author
Gigli, Nicola; Maas, JanIST Austria
Abstract
This paper continues the investigation of `Wasserstein-like' transportation distances for probability measures on discrete sets. We prove that the discrete transportation metrics on the d-dimensional discrete torus with mesh size 1/N converge, when N→∞, to the standard 2-Wasserstein distance W_2 on the continuous torus in the sense of Gromov-Hausdorff. This is the first convergence result for the recently developed discrete transportation metrics. The result shows the compatibility between these metrics and the well-established 2-Wasserstein metric.
Publishing Year
Date Published
2013-01-01
Journal Title
SIAM Journal on Mathematical Analysis
Acknowledgement
JM acknowledges support by Rubicon subsidy 680-50-0901 of the Netherlands Organisation for Scientific Research (NWO).
Volume
45
Issue
2
Page
879 - 899
IST-REx-ID

Cite this

Gigli N, Maas J. Gromov-Hausdorff convergence of discrete transportation metrics. SIAM Journal on Mathematical Analysis. 2013;45(2):879-899. doi:10.1137/120886315
Gigli, N., & Maas, J. (2013). Gromov-Hausdorff convergence of discrete transportation metrics. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/120886315
Gigli, Nicola, and Jan Maas. “Gromov-Hausdorff Convergence of Discrete Transportation Metrics.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics , 2013. https://doi.org/10.1137/120886315 .
N. Gigli and J. Maas, “Gromov-Hausdorff convergence of discrete transportation metrics,” SIAM Journal on Mathematical Analysis, vol. 45, no. 2. Society for Industrial and Applied Mathematics , pp. 879–899, 2013.
Gigli N, Maas J. 2013. Gromov-Hausdorff convergence of discrete transportation metrics. SIAM Journal on Mathematical Analysis. 45(2), 879–899.
Gigli, Nicola, and Jan Maas. “Gromov-Hausdorff Convergence of Discrete Transportation Metrics.” SIAM Journal on Mathematical Analysis, vol. 45, no. 2, Society for Industrial and Applied Mathematics , 2013, pp. 879–99, doi:10.1137/120886315 .
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