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The random batch method provides an efficient algorithm for computing statistical properties of a canonical ensemble of interacting particles. In this work, we study the error estimates of the fully discrete random batch method, especially…

Probability · Mathematics 2022-09-01 Xuda Ye , Zhennan Zhou

The random batch method [J. Comput. Phys. 400 (2020) 108877] is not only an efficient algorithm for simulation of classical $N$-particle systems and their mean-field limit, but also a new model for interacting particle system that could be…

Numerical Analysis · Mathematics 2025-05-20 Lei Li , Yuelin Wang , Shi Jin

We consider a $N$-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system.…

Analysis of PDEs · Mathematics 2018-08-01 José A. Carrillo , Young-Pil Choi , Samir Salem

We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: it has the same weak limit as…

Probability · Mathematics 2026-03-24 Nikolaos Kolliopoulos , Martin Larsson , Zeyu Zhang

We consider a system of classical Brownian particles interacting via a smooth long-range potential in the mean-field regime, and we analyze the propagation of chaos in form of sharp, uniform-in-time estimates on many-particle correlation…

Analysis of PDEs · Mathematics 2025-02-18 Armand Bernou , Mitia Duerinckx

The trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation in the presence of a convex external potential, without smallness restriction on the interaction. From this are…

Probability · Mathematics 2017-09-11 Pierre Monmarché

We use out-of-time-order commutator (OTOC) to diagnose the propagation of chaos in one dimensional long-range power law interaction system. We map the evolution of OTOC to a classical stochastic dynamics problem and use a Brownian quantum…

Statistical Mechanics · Physics 2019-08-12 Xiao Chen , Tianci Zhou

Introduced in 2017 \cite{B1-pinnau2017consensus}, Consensus-Based Optimization (CBO) has rapidly emerged as a significant breakthrough in global optimization. This straightforward yet powerful multi-particle, zero-order optimization method…

Analysis of PDEs · Mathematics 2025-05-29 Massimo Fornasier , Lukang Sun

In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…

Optimization and Control · Mathematics 2021-11-23 Giacomo Borghi , Michael Herty , Lorenzo Pareschi

We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…

Probability · Mathematics 2026-05-06 Solesne Bourguin , Konstantinos Spiliopoulos

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 study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call 'probabilistic solution' a weak solution which remains a cumulative distribution function at all…

Probability · Mathematics 2014-03-13 Benjamin Jourdain , Julien Reygner

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 prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…

Analysis of PDEs · Mathematics 2024-10-18 Jose Antonio Carrillo , Shuchen Guo

We investigate propagation of chaos for mean field Markov Decision Process with common noise (CMKV-MDP), and when the optimization is performed over randomized open-loop controls on infinite horizon. We first state a rate of convergence of…

Optimization and Control · Mathematics 2022-07-27 Médéric Motte , Huyên Pham

Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that…

Optimization and Control · Mathematics 2026-05-15 Giacomo Borghi , José A. Carrillo

We study properties of chaos in generic one-dimensional nonlinear Hamiltonian lattices comprised of weakly coupled nonlinear oscillators, by numerical simulations of continuous-time systems and symplectic maps. For small coupling, the…

Chaotic Dynamics · Physics 2011-12-06 Mario Mulansky , Karsten Ahnert , Arkady Pikovsky , Dima Shepelyansky

A self-interacting dynamics that mimics the standard Consensus-Based Optimization (CBO) model is introduced. This single-particle dynamics is shown to converge to a unique invariant measure that approximates the global minimum of a given…

Optimization and Control · Mathematics 2024-11-18 Hui Huang , Hicham Kouhkouh

In this paper, we study consensus-based optimization (CBO), which is a multi-agent metaheuristic derivative-free optimization method that can globally minimize nonconvex nonsmooth functions and is amenable to theoretical analysis. Based on…

Numerical Analysis · Mathematics 2024-09-10 Massimo Fornasier , Timo Klock , Konstantin Riedl

In this article, we prove the first quantitative uniform in time propagation of chaos for a class of systems of particles in singular repulsive interaction in dimension one that contains the Dyson Brownian motion. We start by establishing…

Probability · Mathematics 2022-04-25 Arnaud Guillin , Pierre Le Bris , Pierre Monmarché