Mean Field Limit and Propagation of Chaos for Vlasov Systems with Bounded Forces

By Pierre-Emmanuel Jabin, Zhenfu Wang. 2015

154 citations recorded by the source corpus.

We consider large systems of particles interacting through rough but bounded interaction kernels. We are able to control the relative entropy between the $N$-particle distribution and the expected limit which solves the corresponding Vlasov system. This implies the Mean Field limit to the Vlasov system together with Propagation of Chaos through the strong convergence of all the marginals. The method works at the level of the Liouville equation and relies on precise combinatorics results.

Subfields: Applied Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e1ee298143b2e30eb5c7548fcc5cee34e2b01764

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In Applied Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions (2021, methodology): “Note that there is no normalization by the dimension in our definitions ofH andWp, in contrast to [32, 34, 48, 28].”
Quantitative estimates of propagation of chaos for stochastic systems with W-1,∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{d (2017, methodology): “It has also been proved to be quite complex: From a technical point of view, the whole combinatorics estimates of [29] can be summarized in section 3 of the present article while the new estimates are considerably longer, see section 5.”
On mean-field limits and quantitative estimates with a large class of singular kernels: Application to the Patlak–Keller–Segel model (2019, methodology): “is exactly the relative entropy introduced in [17,18] and KN(G N |G ρ̄N ) = − 1 N ∫”
On the convergence of closed-loop Nash equilibria to the mean field game limit (2018, background): “5 5Aside from [51], some other papers have developed propagation of chaos results in total variation, such as [3, 42].”
Mean Field Limit for Stochastic Particle Systems (2017, methodology): “Finally, in section 4 we briefly review the authors’ recent results [47] and [48] for very rough interaction kernels K with the relative entropy method.”