{"abstract":[{"text":"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. \n\n\n","lang":"eng"}],"publication":"SIAM Journal on Mathematical Analysis","publication_status":"published","issue":"2","title":"Gromov-Hausdorff convergence of discrete transportation metrics","quality_controlled":0,"author":[{"last_name":"Gigli","first_name":"Nicola","full_name":"Gigli, Nicola"},{"last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","full_name":"Jan Maas","orcid":"0000-0002-0845-1338"}],"doi":"10.1137/120886315 ","main_file_link":[{"url":"http://arxiv.org/abs/1207.6501","open_access":"1"}],"_id":"2129","intvolume":"        45","type":"journal_article","extern":1,"volume":45,"date_updated":"2021-01-12T06:55:29Z","publist_id":"4904","oa":1,"date_published":"2013-01-01T00:00:00Z","day":"01","page":"879 - 899","status":"public","year":"2013","publisher":"Society for Industrial and Applied Mathematics ","date_created":"2018-12-11T11:55:53Z","month":"01","citation":{"ieee":"N. Gigli and J. Maas, “Gromov-Hausdorff convergence of discrete transportation metrics,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 45, no. 2. Society for Industrial and Applied Mathematics , pp. 879–899, 2013.","ama":"Gigli N, Maas J. Gromov-Hausdorff convergence of discrete transportation metrics. <i>SIAM Journal on Mathematical Analysis</i>. 2013;45(2):879-899. doi:<a href=\"https://doi.org/10.1137/120886315 \">10.1137/120886315 </a>","mla":"Gigli, Nicola, and Jan Maas. “Gromov-Hausdorff Convergence of Discrete Transportation Metrics.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 45, no. 2, Society for Industrial and Applied Mathematics , 2013, pp. 879–99, doi:<a href=\"https://doi.org/10.1137/120886315 \">10.1137/120886315 </a>.","short":"N. Gigli, J. Maas, SIAM Journal on Mathematical Analysis 45 (2013) 879–899.","apa":"Gigli, N., &#38; Maas, J. (2013). Gromov-Hausdorff convergence of discrete transportation metrics. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics . <a href=\"https://doi.org/10.1137/120886315 \">https://doi.org/10.1137/120886315 </a>","ista":"Gigli N, Maas J. 2013. Gromov-Hausdorff convergence of discrete transportation metrics. SIAM Journal on Mathematical Analysis. 45(2), 879–899.","chicago":"Gigli, Nicola, and Jan Maas. “Gromov-Hausdorff Convergence of Discrete Transportation Metrics.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics , 2013. <a href=\"https://doi.org/10.1137/120886315 \">https://doi.org/10.1137/120886315 </a>."},"acknowledgement":"JM acknowledges support by Rubicon subsidy 680-50-0901 of the Netherlands Organisation for Scientific Research (NWO)."}