{"issue":"3","oa":1,"author":[{"last_name":"Gladbach","full_name":"Gladbach, Peter","first_name":"Peter"},{"first_name":"Eva","full_name":"Kopfer, Eva","last_name":"Kopfer"},{"last_name":"Maas","full_name":"Maas, Jan","first_name":"Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"intvolume":"        52","article_processing_charge":"No","oa_version":"Preprint","doi":"10.1137/19M1243440","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"JaMa"}],"publication_identifier":{"issn":["00361410"],"eissn":["10957154"]},"abstract":[{"text":"We consider dynamical transport metrics for probability measures on discretisations of a bounded convex domain in ℝd. These metrics are natural discrete counterparts to the Kantorovich metric 𝕎2, defined using a Benamou-Brenier type formula. Under mild assumptions we prove an asymptotic upper bound for the discrete transport metric Wt in terms of 𝕎2, as the size of the mesh T tends to 0. However, we show that the corresponding lower bound may fail in general, even on certain one-dimensional and symmetric two-dimensional meshes. In addition, we show that the asymptotic lower bound holds under an isotropy assumption on the mesh, which turns out to be essentially necessary. This assumption is satisfied, e.g., for tilings by convex regular polygons, and it implies Gromov-Hausdorff convergence of the transport metric.","lang":"eng"}],"date_published":"2020-10-01T00:00:00Z","date_updated":"2023-09-18T08:13:15Z","_id":"71","publication":"SIAM Journal on Mathematical Analysis","external_id":{"arxiv":["1809.01092"],"isi":["000546975100017"]},"volume":52,"status":"public","article_type":"original","scopus_import":"1","day":"01","isi":1,"type":"journal_article","publisher":"Society for Industrial and Applied Mathematics","publist_id":"7983","main_file_link":[{"url":"https://arxiv.org/abs/1809.01092","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","month":"10","quality_controlled":"1","title":"Scaling limits of discrete optimal transport","date_created":"2018-12-11T11:44:28Z","page":"2759-2802","year":"2020","citation":{"chicago":"Gladbach, Peter, Eva Kopfer, and Jan Maas. “Scaling Limits of Discrete Optimal Transport.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2020. <a href=\"https://doi.org/10.1137/19M1243440\">https://doi.org/10.1137/19M1243440</a>.","ista":"Gladbach P, Kopfer E, Maas J. 2020. Scaling limits of discrete optimal transport. SIAM Journal on Mathematical Analysis. 52(3), 2759–2802.","apa":"Gladbach, P., Kopfer, E., &#38; Maas, J. (2020). Scaling limits of discrete optimal transport. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/19M1243440\">https://doi.org/10.1137/19M1243440</a>","ieee":"P. Gladbach, E. Kopfer, and J. Maas, “Scaling limits of discrete optimal transport,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 3. Society for Industrial and Applied Mathematics, pp. 2759–2802, 2020.","mla":"Gladbach, Peter, et al. “Scaling Limits of Discrete Optimal Transport.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 3, Society for Industrial and Applied Mathematics, 2020, pp. 2759–802, doi:<a href=\"https://doi.org/10.1137/19M1243440\">10.1137/19M1243440</a>.","ama":"Gladbach P, Kopfer E, Maas J. Scaling limits of discrete optimal transport. <i>SIAM Journal on Mathematical Analysis</i>. 2020;52(3):2759-2802. doi:<a href=\"https://doi.org/10.1137/19M1243440\">10.1137/19M1243440</a>","short":"P. Gladbach, E. Kopfer, J. Maas, SIAM Journal on Mathematical Analysis 52 (2020) 2759–2802."}}