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In this paper we derive a two dimensional spray model with gyroscopic effects as the mean-field limit of a system modeling the interaction between an incompressible fluid and a finite number of solid particles. This spray model has been…

Analysis of PDEs · Mathematics 2023-07-11 Matthieu Ménard

We present a unified framework, with quantitative estimates, for deterministic interacting particle systems whose pairwise interactions may depend on heterogeneous labels. Heterogeneity is kept at every level by adding a frozen label…

Analysis of PDEs · Mathematics 2026-05-21 Thierry Paul , Emmanuel Trélat

The paper treats the validity problem of the nonrelativistic Vlasov-Poisson equation in $d\geq 2$ dimensions. It is shown that the Vlasov-Poisson dynamics can be derived as a combined mean field and point-particle limit of an N-particle…

Mathematical Physics · Physics 2016-03-23 Dustin Lazarovici

We present a new proof of the convergence of the N-particle Schroedinger dynamics for bosons towards the dynamics generated by the Hartree equation in the mean-field limit. For a restricted class of two-body interactions, we obtain…

Mathematical Physics · Physics 2016-08-16 Juerg Froehlich , Sandro Graffi , Simon Schwarz

This paper is concerned with the mean-field limit for the gradient flow evolution of particle systems with pairwise Riesz interactions, as the number of particles tends to infinity. Based on a modulated energy method, using regularity and…

Analysis of PDEs · Mathematics 2016-07-06 Mitia Duerinckx

We discuss the construction and approximation of solutions to a nonlinear McKean-Vlasov equation driven by a singular self-excitatory interaction of the mean-field type. Such an equation is intended to describe an infinite population of…

Probability · Mathematics 2015-01-26 F. Delarue , J. Inglis , S. Rubenthaler , E. Tanré

This article aims to study coupled mean-field equation and ODEs with discrete events motivated by vehicular traffic flow. Precisely, multi-lane traffic flow in presence of human-driven and autonomous vehicles is considered, with the…

Analysis of PDEs · Mathematics 2021-10-22 Xiaoqian Gong , Benedetto Piccoli , Giuseppe Visconti

We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and attractive cross-interaction. After providing a suitable…

Analysis of PDEs · Mathematics 2020-08-26 Marco Di Francesco , Antonio Esposito , Markus Schmidtchen

We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such problems arise naturally as ${\Gamma}$-limits of optimal control problems subject to ODE…

Optimization and Control · Mathematics 2015-04-10 Mattia Bongini , Massimo Fornasier , Francesco Rossi , Francesco Solombrino

In this paper we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in~\cite{DuncanPavliotis2016}. We…

Statistical Mechanics · Physics 2018-01-17 S. N. Gomes , G. A. Pavliotis

We analyze the mean-field limit of a stochastic Schr{\"o}dinger equation arising in quantum optimal control and mean-field games, where N interacting particles undergo continuous indirect measurement. For the open quantum system described…

Analysis of PDEs · Mathematics 2025-07-28 Anne de Bouard , Gaoyue Guo , Théo Hérouard

This paper deals with the derivation of the mean-field limit for multi-agent systems on a large class of sparse graphs. More specifically, the case of non-exchangeable multi-agent systems consisting of non-identical agents is addressed. The…

Probability · Mathematics 2025-11-21 Pierre-Emmanuel Jabin , David Poyato , Juan Soler

In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…

Analysis of PDEs · Mathematics 2019-09-25 Jose A. Carrillo , Edgard A. Pimentel , Vardan K. Voskanyan

In this paper, we derive the mean-field limit of a collective dynamics model with time-varying weights, for weight dynamics that preserve the total mass of the system as well as indistinguishability of the agents. The limit equation is a…

Analysis of PDEs · Mathematics 2021-03-12 Nastassia Pouradier Duteil

We consider a system of $N$ interacting particles, governed by transport and diffusion, that converges in a mean-field limit to the solution of a McKean-Vlasov equation. From the observation of a trajectory of the system over a fixed time…

Statistics Theory · Mathematics 2021-03-16 Laetitia Della Maestra , Marc Hoffmann

In this paper we study the mean-field limit of a system of point vortices for the lake equations. These equations model the evolution of the horizontal component of the velocity field of a fluid in a lake of non-constant depth, when its…

Analysis of PDEs · Mathematics 2023-09-20 Matthieu Ménard

We consider particle-based stochastic reaction-drift-diffusion models where particles move via diffusion and drift induced by one- and two-body potential interactions. The dynamics of the particles are formulated as measure-valued…

Probability · Mathematics 2025-01-22 Max Heldman , Samuel A. Isaacson , Qianhan Liu , Konstantinos Spiliopoulos

We study the mean field limit of one-particle reduced density matrices, for a bosonic system in an initial state with a fixed number of particles, only a fraction of which occupies the same state, and for linear combinations of such states.…

Mathematical Physics · Physics 2013-05-27 Marco Falconi

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

Probability · Mathematics 2020-11-03 Masaaki Fujii

We consider a one-dimensional McKean-Vlasov SDE on a domain and the associated mean-field interacting particle system. The peculiarity of this system is the combination of the interaction, which keeps the average position prescribed, and…

Probability · Mathematics 2024-02-29 Michele Coghi , Wolfgang Dreyer , Paul Gajewski , Clemens Guhlke , Peter Friz , Mario Maurelli