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In this work, we consider one-dimensional particles interacting in mean-field type through a bounded kernel. In addition, when particles hit some barrier (say zero), they are removed from the system. This absorption of particles is…

Probability · Mathematics 2026-04-07 Gaoyue Guo , Maxime Latypov , Milica Tomasevic

We consider the continuous version of the Vicsek model with noise, proposed as a model for collective behavior of individuals with a fixed speed. We rigorously derive the kinetic mean-field partial differential equation satisfied when the…

Probability · Mathematics 2011-12-06 François Bolley , José A. Cañizo , José A. Carrillo

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 describe the macroscopic behaviour of a particle system with long-range interactions. We describe conditions on the interaction strength in dependency of the distance of the particles, such that the scaling limit of the particle system…

Probability · Mathematics 2015-12-21 Anton Bovier , Carina Geldhauser

We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…

Probability · Mathematics 2022-04-19 Alexander Stolyar

Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…

Analysis of PDEs · Mathematics 2025-07-30 Sebastian Throm

This note is a companion article to the recent paper L\"ocherbach, Loukianova, Marini (2024). We consider mean field systems of interacting particles. Each particle jumps with a jump rate depending on its position. When jumping, a…

Probability · Mathematics 2024-07-02 Dasha Loukianova , Eva Löcherbach

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

This paper addresses congested transport, which can be described, at macroscopic scales, by a continuity equation with a pressure variable generated from the hard-congestion constraint (maximum value of the density). The main goal of the…

Analysis of PDEs · Mathematics 2024-05-27 Inwon Kim , Antoine Mellet , Jeremy Sheung-Him Wu

We study so-called supercritical mean-field limits of systems of trapped particles moving according to Newton's second law with either Coulomb/super-Coulomb or regular interactions, from which we derive a $\mathsf{d}$-dimensional…

Analysis of PDEs · Mathematics 2024-08-28 Matthew Rosenzweig , Sylvia Serfaty

Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with…

Probability · Mathematics 2018-02-05 Franco Flandoli , Enrico Priola , Giovanni Zanco

This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…

Probability · Mathematics 2025-10-07 Louis-Pierre Chaintron , Antoine Diez

In this paper, we are concerned with a class of conservative systems including asymmetric exclusion processes and zero-range processes as examples, where some particles are initially placed on $N$ positions. A particle jumps from a position…

Probability · Mathematics 2024-01-24 Xiaofeng Xue

We study an interacting particle system in $\mathbf{R}^d$ motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling from a given probability density with unknown normalization.…

Analysis of PDEs · Mathematics 2018-11-07 Jianfeng Lu , Yulong Lu , James Nolen

Interacting particle systems are known for their ability to generate large-scale self-organized structures from simple local interaction rules between each agent and its neighbors. In addition to studying their emergent behavior, a main…

Analysis of PDEs · Mathematics 2024-10-21 Nathalie Ayi , Nastassia Pouradier Duteil , David Poyato

We consider a coupled system composed of a linear differential-algebraic equation (DAE) and a linear large-scale system of ordinary differential equations where the latter stands for the dynamics of numerous identical particles. Replacing…

Numerical Analysis · Mathematics 2020-11-02 Steffen Plunder , Bernd Simeon

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 study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…

Probability · Mathematics 2021-07-21 Watthanan Jatuviriyapornchai , Stefan Grosskinsky

We consider a system consisting of $n$ particles, moving forward in jumps on the real line. System state is the empirical distribution of particle locations. Each particle ``jumps forward'' at some time points, with the instantaneous rate…

Probability · Mathematics 2023-03-03 Alexander Stolyar

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
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