---
_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'
...