Repository: Freie Universit├Ąt Berlin, Math Department

From large deviations to Wasserstein gradient flows in multiple dimensions

Erbar, M. and Maas, J. and Renger, M. (2015) From large deviations to Wasserstein gradient flows in multiple dimensions. Electronic Communications in Probability, 20 (89).

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Abstract

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) 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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:1876
Deposited By: Ulrike Eickers
Deposited On:16 Mar 2016 09:27
Last Modified:03 Mar 2017 14:42

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