Filters

20151

More filters

20191
Reset filters

Settings

Author: Erbar, Matthias × Subject: Gamma convergence ×

Search Results

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    From large deviations to Wasserstein gradient flows in multiple dimensions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Erbar, Matthias; Maas, Jan; Renger, D.R. Michiel
    We study the large deviation rate functional for the empirical measure of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier and Zimmer [ADPZ11] that this functional is asymptotically equivalent (in the sense of -convergence) to the JordanKinderlehrerOtto functional arising in the Wasserstein gradient flow structure of the FokkerPlanck 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 in [DLR13] 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 [ADPZ11] to arbitrary dimensions.