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Related papers: A mean field limit for the Vlasov-Poisson system

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We consider the relativistic Vlasov-Maxwell system in three dimensions and study the limiting asymptotic behavior as $t \to \infty$ of solutions launched by small, compactly supported initial data. In particular, we prove that such…

Analysis of PDEs · Mathematics 2024-03-12 Stephen Pankavich , Jonathan Ben-Artzi

A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a…

Analysis of PDEs · Mathematics 2021-09-20 Li Chen , Alexandra Holzinger , Ansgar Jüngel , Nicola Zamponi

Motivated by several applications, including neuronal models, we consider the McKean-Vlasov limit for mean-field systems of interacting diffusions with simultaneous jumps. We prove propagation of chaos via a coupling technique that involves…

Probability · Mathematics 2017-04-05 Luisa Andreis , Paolo Dai Pra , Markus Fischer

We study the finite Larmor radius regime for the Vlasov-Poisson system. The magnetic field is assumed to be uniform. We investigate this non linear problem in the two dimensional setting. We derive the limit model by appealing to…

Analysis of PDEs · Mathematics 2015-11-03 Mihaï Bostan , Aurélie Finot , Maxime Hauray

In this note, we consider generalizations of the Cucker-Smale dynamical system and we derive rigorously in Wasserstein's type topologies the mean-field limit (and propagation of chaos) to the Vlasov-type equation introduced in [12].Unlike…

Analysis of PDEs · Mathematics 2021-02-10 Roberto Natalini , Thierry Paul

The mean-field limit for systems of self-propelled agents with topological interaction cannot be obtained by means of the usual Dobrushin approach. We get a result on this direction by adapting to the multidimensional case the techniques…

Analysis of PDEs · Mathematics 2021-12-01 Dario Benedetto , Emanuele Caglioti , Stefano Rossi

The physical essence of the non-relativistic limit, from the relativistic Vlasov-Maxwell-Landau system to the Vlasov-Poisson-Landau system, lies in the transition from finite-speed electromagnetic waves to instantaneous Coulomb…

Analysis of PDEs · Mathematics 2025-11-25 Chuqi Cao , Ling-Bing He , Yuanjie Lei , Qinghua Xiao

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

We consider the dynamics of $N$ interacting bosons in three dimensions which are strongly confined in one or two directions. We analyze the two cases where the interaction potential $w$ is rescaled by either $N^{-1}w(\cdot)$ or…

Mathematical Physics · Physics 2014-12-11 Johannes von Keler

In this work, we prove the well--posedness of a singularly interacting stochastic particle system and we establish propagation of chaos result towards the one-dimensional parabolic-parabolic Keller-Segel model.

Probability · Mathematics 2018-10-17 Jean-Francois Jabir , Denis Talay , Milica Tomasevic

In this paper, we consider the mean field limit of Brownian particles with Coulomb interaction in 3D space. In particular, using a symmetrization technique, we show that the limit measure almost surely is a weak solution to the limiting…

Analysis of PDEs · Mathematics 2020-01-08 Lei Li , Jian-Guo Liu , Pu Yu

In this work, we study the mean field Schr\"odinger problem from a purely probabilistic point of view by exploiting its connection to stochastic control theory for McKean-Vlasov diffusions. Our main result shows that the mean field…

Probability · Mathematics 2024-09-27 Camilo Hernández , Ludovic Tangpi

We consider the three-dimensional semi-relativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we…

Mathematical Physics · Physics 2009-11-13 Gonca L. Aki , Peter A. Markowich , Christof Sparber

In this paper, we investigate gradient estimate of the Poisson equation and the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$, uniform in the number of particles, and uniform-in-time propagation of chaos for the…

Probability · Mathematics 2021-09-15 Wei Liu , Liming Wu , Chaoen Zhang

In this article we study a system of $N$ particles, each of them being defined by the couple of a position (in $\mathbb{R}^d$) and a so-called orientation which is an element of a compact Riemannian manifold. This orientation can be seen as…

Probability · Mathematics 2021-06-30 Antoine Diez

We develop a mean-field theory for large, non-exchangeable particle (agent) systems where the states and interaction weights co-evolve in a coupled system of SDEs. A first main result is the establishment of the propagation of…

Probability · Mathematics 2025-12-30 Datong Zhou

We consider the N-body Schr\"{o}dinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work \cite{AmNi}, the mean field limit is translated into a semiclassical problem with a…

Mathematical Physics · Physics 2015-05-13 Z. Ammari , F. Nier

We show propagation of moments in velocity for the 3-dimensional Vlasov-Poisson system with a uniform magnetic field $B = (0, 0, {\omega})$ by adapting the work of Lions, Perthame. The added magnetic field also produces singularities at…

Analysis of PDEs · Mathematics 2020-12-22 Alexandre Rege

Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…

Probability · Mathematics 2025-01-07 Lei Li , Yuelin Wang , Yuliang Wang

In this paper, quantitative propagation of chaos in $L^\eta$($\eta\in(0,1]$)-Wasserstein distance for mean field interacting particle system is derived, where the diffusion coefficient is allowed to be interacting and the initial…

Probability · Mathematics 2024-08-30 Xing Huang