--- _id: '1517' abstract: - lang: eng text: "We study the large deviation rate functional for the empirical distribution of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier and Zimmer that this functional is asymptotically equivalent (in the sense of Γ-convergence) to the Jordan-Kinderlehrer-Otto functional arising in the Wasserstein gradient flow structure of the Fokker-Planck equation. In higher dimensions, part of this statement (the lower bound) has been recently proved by Duong, Laschos and Renger, but the upper bound remained open, since the proof of Duong et al relies on regularity properties of optimal transport maps that are restricted to one dimension. In this note we present a new proof of the upper bound, thereby generalising the result of Adams et al to arbitrary dimensions.\r\n" article_number: '89' author: - first_name: Matthias full_name: Erbar, Matthias last_name: Erbar - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Michiel full_name: Renger, Michiel last_name: Renger citation: ama: Erbar M, Maas J, Renger M. From large deviations to Wasserstein gradient flows in multiple dimensions. Electronic Communications in Probability. 2015;20. doi:10.1214/ECP.v20-4315 apa: Erbar, M., Maas, J., & Renger, M. (2015). From large deviations to Wasserstein gradient flows in multiple dimensions. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/ECP.v20-4315 chicago: Erbar, Matthias, Jan Maas, and Michiel Renger. “From Large Deviations to Wasserstein Gradient Flows in Multiple Dimensions.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2015. https://doi.org/10.1214/ECP.v20-4315. ieee: M. Erbar, J. Maas, and M. Renger, “From large deviations to Wasserstein gradient flows in multiple dimensions,” Electronic Communications in Probability, vol. 20. Institute of Mathematical Statistics, 2015. ista: Erbar M, Maas J, Renger M. 2015. From large deviations to Wasserstein gradient flows in multiple dimensions. Electronic Communications in Probability. 20, 89. mla: Erbar, Matthias, et al. “From Large Deviations to Wasserstein Gradient Flows in Multiple Dimensions.” Electronic Communications in Probability, vol. 20, 89, Institute of Mathematical Statistics, 2015, doi:10.1214/ECP.v20-4315. short: M. Erbar, J. Maas, M. Renger, Electronic Communications in Probability 20 (2015). date_created: 2018-12-11T11:52:29Z date_published: 2015-11-29T00:00:00Z date_updated: 2021-01-12T06:51:19Z day: '29' ddc: - '519' department: - _id: JaMa doi: 10.1214/ECP.v20-4315 file: - access_level: open_access checksum: 135741c17d3e1547ca696b6fbdcd559c content_type: application/pdf creator: system date_created: 2018-12-12T10:10:39Z date_updated: 2020-07-14T12:45:00Z file_id: '4828' file_name: IST-2016-494-v1+1_4315-23820-1-PB.pdf file_size: 230525 relation: main_file file_date_updated: 2020-07-14T12:45:00Z has_accepted_license: '1' intvolume: ' 20' language: - iso: eng month: '11' oa: 1 oa_version: Published Version publication: Electronic Communications in Probability publication_status: published publisher: Institute of Mathematical Statistics publist_id: '5660' pubrep_id: '494' quality_controlled: '1' scopus_import: 1 status: public title: From large deviations to Wasserstein gradient flows in multiple dimensions tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 20 year: '2015' ...