Gromov-Hausdorff convergence of discrete transportation metrics Journal Article

Author(s): Gigli, Nicola; Maas, Jan
Article Title: Gromov-Hausdorff convergence of discrete transportation metrics
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 Nā†’āˆž, 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.
Keywords: Discrete transportation metric; Gromov-hausdorf convergence; Wasserstein metric
Journal Title: SIAM Journal on Mathematical Analysis
Volume: 45
Issue 2
ISSN: 1095-7154
Publisher: Society for Industrial and Applied Mathematics  
Date Published: 2013-01-01
Start Page: 879
End Page: 899
Sponsor: JM acknowledges support by Rubicon subsidy 680-50-0901 of the Netherlands Organisation for Scientific Research (NWO).
DOI: 10.1137/120886315
Open access: yes (repository)
IST Austria Authors
  1. Jan Maas
    28 Maas