@article{2129, 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. }, author = {Gigli, Nicola and Jan Maas}, journal = {SIAM Journal on Mathematical Analysis}, number = {2}, pages = {879 -- 899}, publisher = {Society for Industrial and Applied Mathematics }, title = {{Gromov-Hausdorff convergence of discrete transportation metrics}}, doi = {10.1137/120886315 }, volume = {45}, year = {2013}, }