A λ-convexity based proof for the propagation of chaos for weakly interacting stochastic particles
File(s)
OA Location
Author(s)
Carrillo, JA
Delgadino, MG
Pavliotis, GA
Type
Journal Article
Abstract
In this work we give a proof of the mean-field limit for λ-convex potentials using a purely variational viewpoint. Our approach is based on the observation that all evolution equations that we study can be written as gradient flows of functionals at different levels: in the set of probability measures, in the set of symmetric probability measures on N variables, and in the set of probability measures on probability measures. This basic fact allows us to rely on Γ-convergence tools for gradient flows to complete the proof by identifying the limits of the different terms in the Evolutionary Variational Inequalities (EVIs) associated to each gradient flow. The λ-convexity of the confining and interaction potentials is crucial for the unique identification of the limits and for deriving the EVIs at each description level of the interacting particle system.
Date Issued
2020-12-01
Date Acceptance
2020-08-04
Citation
Journal of Functional Analysis, 2020, 279 (10), pp.1-30
ISSN
0022-1236
Publisher
Elsevier BV
Start Page
1
End Page
30
Journal / Book Title
Journal of Functional Analysis
Volume
279
Issue
10
Copyright Statement
© 2020 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://www.sciencedirect.com/science/article/pii/S0022123620302779?via%3Dihub
Grant Number
EP/L020564/1
EP/L024926/1
EP/P031587/1
Subjects
Science & Technology
Physical Sciences
Mathematics
Gradient flows
Propagation of chaos
Gamma-convergence
STATISTICAL-MECHANICS
GRADIENT FLOWS
METRIC-SPACES
CONVERGENCE
EQUILIBRIUM
0101 Pure Mathematics
General Mathematics
Publication Status
Published
Article Number
ARTN 108734
Date Publish Online
2020-08-11