From a large-deviations principle to the Wasserstein gradient flow : a new micro-macro passage
Adams, S. (Stefan), Dirr, Nicolas, Peletier, M. A. (Mark A.) and Zimmer, Johannes. (2011) From a large-deviations principle to the Wasserstein gradient flow : a new micro-macro passage. Communications in Mathematical Physics, Vol.307 (No.3). pp. 791-815. ISSN 0010-3616Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s00220-011-1328-4
We study the connection between a system of many independent Brownian particles on one hand and the deterministic diffusion equation on the other. For a fixed time step h > 0, a large-deviations rate functional J h characterizes the behaviour of the particle system at t = h in terms of the initial distribution at t = 0. For the diffusion equation, a single step in the time-discretized entropy-Wasserstein gradient flow is characterized by the minimization of a functional K h . We establish a new connection between these systems by proving that J h and K h are equal up to second order in h as h → 0. This result gives a microscopic explanation of the origin of the entropy-Wasserstein gradient flow formulation of the diffusion equation. Simultaneously, the limit passage presented here gives a physically natural description of the underlying particle system by describing it as an entropic gradient flow.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Library of Congress Subject Headings (LCSH):||Large deviations, Mathematical physics|
|Journal or Publication Title:||Communications in Mathematical Physics|
|Official Date:||November 2011|
|Page Range:||pp. 791-815|
|Access rights to Published version:||Restricted or Subscription Access|
[AGS05] Ambrosio, L., Gigli, N., Savaré, G.: Gradient Flows in Metric Spaces and in the Space of Probability
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