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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…

Probability · Mathematics 2018-05-30 Alain Durmus , Andreas Eberle , Arnaud Guillin , Raphael Zimmer

In this paper, uniform in time quantitative propagation of chaos in $L^1$-Wasserstein distance for mean field interacting particle system is derived, where the diffusion coefficient is allowed to be interacting and the drift is assumed to…

Probability · Mathematics 2025-10-29 Xing Huang

We study the long time behavior of second order particle systems interacting through global Lipschitz kernels. Combining hypocoercivity method in [37] and relative entropy method in [25], we are able to overcome the degeneracy of diffusion…

Analysis of PDEs · Mathematics 2024-09-05 Yun Gong , Zhenfu Wang , Pengzhi Xie

We consider a $N$-particle interacting particle system with the vision geometrical constraints and reflected noises, proposed as a model for collective behavior of individuals. We rigorously derive a continuity-type of mean-field equation…

Analysis of PDEs · Mathematics 2017-05-12 Young-Pil Choi , Samir Salem

We study the mean field Langevin dynamics and the associated particle system. By assuming the functional convexity of the energy, we obtain the $L^p$-convergence of the marginal distributions towards the unique invariant measure for the…

Probability · Mathematics 2025-11-06 Fan Chen , Zhenjie Ren , Songbo Wang

We study the kinetic mean field Langevin dynamics under the functional convexity assumption of the mean field energy functional. Using hypocoercivity, we first establish the exponential convergence of the mean field dynamics and then show…

Probability · Mathematics 2024-02-09 Fan Chen , Yiqing Lin , Zhenjie Ren , Songbo Wang

We consider a $N$-particle model describing an alignment mechanism due to a topological interaction among the agents. We show that the kinetic equation, expected to hold in the mean-field limit $N \to \infty$, as following from the previous…

Mathematical Physics · Physics 2018-03-07 Pierre Degond , Mario Pulvirenti

This paper presents an elementary proof of quantitative uniform-in-time propagation of chaos for the Cucker--Smale model under sufficiently strong interaction. The idea is to combine existing finite-time propagation of chaos estimates with…

Probability · Mathematics 2025-11-03 Nicolai Jurek Gerber , Urbain Vaes

Many low temperature particle systems in mean-field interaction are ergodic with respect to a unique invariant measure, while their (non-linear) mean-field limit may possess several steady states. In particular, in such cases, propagation…

Probability · Mathematics 2025-02-11 Lucas Journel , Pierre Le Bris

This paper is devoted to the study of mean-field limit for systems of indistinguables particles undergoing collision processes. As formulated by Kac \cite{Kac1956} this limit is based on the {\em chaos propagation}, and we (1) prove and…

Analysis of PDEs · Mathematics 2010-01-19 Stéphane Mischler , Clément Mouhot

We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. The limit is given by…

Probability · Mathematics 2021-04-06 Erhan Bayraktar , Ruoyu Wu

We study a nonlocal adhesion model for two interacting tumor cell phenotypes, combining diffusion, pairwise interactions, and random phenotypic switching. The system admits a microscopic diffusion--jump particle description whose mean-field…

Analysis of PDEs · Mathematics 2026-03-16 Myeongju Chae , Young-Pil Choi

Time-uniform log-Sobolev inequalities (LSI) satisfied by solutions of semi-linear mean-field equations have recently appeared to be a key tool to obtain time-uniform propagation of chaos estimates. This work addresses the more general…

Probability · Mathematics 2024-11-08 Pierre Monmarché , Zhenjie Ren , Songbo Wang

In this paper a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method. The model under investigation is an interacting particle system coupled to the eikonal equation…

Analysis of PDEs · Mathematics 2016-11-28 Li Chen , Simone Göttlich , Qitao Yin

We establish general conditions under which there exists uniform in time convergence between a stochastic process and its approximated system. These standardised conditions consist of a local in time estimate between the original and the…

Probability · Mathematics 2024-12-09 Katharina Schuh , Iain Souttar

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

Probability · Mathematics 2025-11-03 Nicolai Jurek Gerber , Franca Hoffmann , Urbain Vaes

We obtain moment and Gaussian bounds for general Lipschitz functions evaluated along the sample path of a Markov chain. We treat Markov chains on general (possibly unbounded) state spaces via a coupling method. If the first moment of the…

Probability · Mathematics 2010-12-08 J. -R. Chazottes , F. Redig

In this article, we study the mean field limit of weakly interacting diffusions for confining and interaction potentials that are not necessarily convex. We explore the relationship between the large $N$ limit of the constant in the…

We study the Fleming-Viot particle process formed by N interacting continuous-time asymmetric random walks on the cycle graph, with uniform killing. We show that this model has a remarkable exact solvability, despite the fact that it is…

Probability · Mathematics 2021-04-13 Josué Corujo

Combining the results of [14] and [10], the trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation. Under some conditions (that allow non-convex confining potentials) the…

Probability · Mathematics 2021-11-17 Arnaud Guillin , Pierre Monmarché
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