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A Collision-Avoiding flocking particle system proposed in [8] is studied in this paper. The global wellposedness of its corresponding Vlasov-type kinetic equation is proved. As a corollary of the global stability result, the mean field…

Mathematical Physics · Physics 2013-11-15 Rong Yang , Li Chen

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

This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…

Optimization and Control · Mathematics 2026-03-31 José A. Carrillo , Shi Jin , Haoyu Zhang , Yuhua Zhu

The random batch method (RBM) proposed in [Jin et al., J. Comput. Phys., 400(2020), 108877] for large interacting particle systems is an efficient with linear complexity in particle numbers and highly scalable algorithm for $N$-particle…

Numerical Analysis · Mathematics 2024-03-14 Zhenyu Huang , Shi Jin , Lei Li

We consider general stochastic systems of interacting particles with noise which are relevant as models for the collective behavior of animals, and rigorously prove that in the mean-field limit the system is close to the solution of a…

Probability · Mathematics 2012-01-12 François Bolley , José Alfredo Cañizo , José Antonio Carrillo

We study the mean-field limit for a class of agent-based models describing flocking with nonlinear velocity alignment. Each agent interacts through a communication protocol $\phi$ and a non-linear coupling of velocities given by the power…

Analysis of PDEs · Mathematics 2026-01-01 Vinh Nguyen , Roman Shvydkoy , Changhui Tan

We consider the Cucker-Smale system with multiplicative noise in a harmonic potential field and investigate the effect of harmonic potential field. In the presence of external potential force, the system is expected to emerge into almost…

Dynamical Systems · Mathematics 2022-05-27 Du Linglong , Zhou Xinyun

We investigate the mean-field limit for interacting particle systems through a duality-based framework and obtain quantitative estimates on the convergence of marginals as well as on correlation functions. In particular, for merely…

Analysis of PDEs · Mathematics 2026-05-05 Nadia Khoury , P. -E. Jabin

In this paper, we present a rigorous derivation of the mean-field limit for a moderately interacting particle system in $\R^d$ $(d\geq 2)$. For stochastic initial data, we demonstrate that the solution to the interacting particle model,…

Analysis of PDEs · Mathematics 2024-07-08 Jinhuan Wang , Mengdi Zhuang , Hui Huang

We consider the collective behaviour of active particles that locally align with their neighbours. Agent-based simulation models have previously shown that in one dimension, these particles can form into a flock that maintains its stability…

Statistical Mechanics · Physics 2018-12-26 Eoin Ó Laighléis , Martin R. Evans , Richard A. Blythe

We propose a large-scale scaling viewpoint for deriving mesoscopic dynamics from interacting particle systems and apply it to the Cucker--Smale flocking model. In contrast with the classical mean-field regime leading to the Vlasov-type…

Analysis of PDEs · Mathematics 2026-02-17 Ruicheng Cheng , Seung-Yeal Ha , Jaemoon Lee , Zhenfu Wang

We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction and diffusion functions from the path of one single particle in the system. Our estimator is obtained by…

Numerical Analysis · Mathematics 2024-01-30 Grigorios A. Pavliotis , Andrea Zanoni

The mean field approximation to the Ising model is a canonical variational tool that is used for analysis and inference in Ising models. We provide a simple and optimal bound for the KL error of the mean field approximation for Ising models…

Machine Learning · Computer Science 2018-02-22 Vishesh Jain , Frederic Koehler , Elchanan Mossel

This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…

Probability · Mathematics 2023-07-21 Anirudh Sridhar , Soummya Kar

We study mean-field particle approximations of normalized Feynman-Kac semi-groups, usually called Fleming-Viot or Feynman-Kac particle systems. Assuming various large time stability properties of the semi-group uniformly in the initial…

Probability · Mathematics 2024-12-23 Lucas Journel , Mathias Rousset

Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be…

Performance · Computer Science 2018-07-24 Nicolas Gast , Diego Latella , Mieke Massink

The Random Batch Method proposed in our previous work [Jin et al., J. Comput. Phys., 400(1), 2020] is not only a numerical method for interacting particle systems and its mean-field limit, but also can be viewed as a model of particle…

Probability · Mathematics 2020-11-24 Shi Jin , Lei Li

The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…

Statistics Theory · Mathematics 2025-02-10 Edoardo Calvello , Pierre Monmarché , Andrew M. Stuart , Urbain Vaes

Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples --…

Machine Learning · Statistics 2026-05-15 Ayoub Belhadji , Daniel Sharp , Youssef M. Marzouk

The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the…

Optimization and Control · Mathematics 2026-02-16 Hui Huang , Jethro Warnett
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