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An elementary approach to uniform in time propagation of chaos


Authors: Alain Durmus, Andreas Eberle, Arnaud Guillin and Raphael Zimmer
Journal: Proc. Amer. Math. Soc. 148 (2020), 5387-5398
MSC (2010): Primary 60J60, 60H10
DOI: https://doi.org/10.1090/proc/14612
Published electronically: September 4, 2020
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Abstract: Based on a coupling approach, we prove uniform in time propagation of chaos for weakly interacting mean-field particle systems with possibly non-convex confinement and interaction potentials. The approach is based on a combination of reflection and synchronous couplings applied to the individual particles. It provides explicit quantitative bounds that significantly extend previous results for the convex case.


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Additional Information

Alain Durmus
Affiliation: CMLA, ENS Cachan, CNRS, Université Paris-Saclay, 94235 Cachan, France
MR Author ID: 1018760
Email: alain.durmus@cmla.ens-cachan.fr

Andreas Eberle
Affiliation: Universität Bonn, Institut für Angewandte Mathematik, Endenicher Allee 60, 53115 Bonn, Germany
MR Author ID: 363836
Email: eberle@uni-bonn.de

Arnaud Guillin
Affiliation: Laboratoire de Mathématiques Blaise Pascal, CNRS - UMR 6620, Université Clermont-Auvergne, Avenue des landais, 63177 Aubiere cedex, France
MR Author ID: 661909
Email: guillin@math.univ-bpclermont.fr

Raphael Zimmer
Affiliation: Universität Bonn, Institut für Angewandte Mathematik, Endenicher Allee 60, 53115 Bonn, Germany
MR Author ID: 1228825
Email: Raphael@infoZimmer.de

DOI: https://doi.org/10.1090/proc/14612
Received by editor(s): October 30, 2018
Published electronically: September 4, 2020
Additional Notes: This work was initiated through a Procope project, which is greatly acknowledged. The work was partially supported by ANR-17-CE40-0030, by the Hausdorff Center for Mathematics, and by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund.
Communicated by: Zhen-Qing Chen
Article copyright: © Copyright 2020 American Mathematical Society