Journal
ELECTRONIC COMMUNICATIONS IN PROBABILITY
Volume 20, Issue -, Pages 1-12Publisher
UNIV WASHINGTON, DEPT MATHEMATICS
DOI: 10.1214/ECP.v20-4315
Keywords
Large deviations; gradient flows; Wasserstein metric; Gamma-convergence
Categories
Funding
- German Research Foundation through the Hausdorff Center for Mathematics at the University of Bonn
- Collaborative Research Centers [1060, 1114]
Ask authors/readers for more resources
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 Gamma-convergence as the time-step goes to zero) 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 their proof of the upper bound 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, Dirr, Peletier and Zimmer to arbitrary dimensions.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available