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The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of…

Mathematical Physics · Physics 2015-06-15 Niels Benedikter , Marcello Porta , Benjamin Schlein

In this paper, we study sufficient conditions for the emergence of asymptotic consensus and flocking in a certain class of non-linear generalised Cucker-Smale systems subject to multiplicative communication failures. Our approach is based…

Optimization and Control · Mathematics 2021-05-04 Benoît Bonnet , Émilien Flayac

The mean-field limit of interacting diffusions without exchangeability, caused by weighted interactions and non-i.i.d. initial values, are investigated. The weights could be signed and unbounded. The result applies to a large class of…

Probability · Mathematics 2026-01-19 Zhenfu Wang , Xianliang Zhao , Rongchan Zhu

We consider a mean-field control problem in which admissible controls are required to be adapted to the common noise filtration. The main objective is to show how the mean-field control problem can be approximates by time consistent…

Optimization and Control · Mathematics 2025-09-19 Bruno Bouchard , Xiaolu Tan

We consider large systems of stochastic interacting particles through discontinuous kernels which has vision geometrical constrains. We rigorously derive a Vlasov-Fokker-Planck type of kinetic mean-field equation from the corresponding…

Analysis of PDEs · Mathematics 2017-05-12 Young-Pil Choi , Samir Salem

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 investigate the pressureless fractional Euler-alignment system with nonlinear velocity couplings, referred to as the $p$-Euler-alignment system. This model features a nonlinear velocity alignment force, interpreted as a density-weighted…

Analysis of PDEs · Mathematics 2024-09-17 Young-Pil Choi , Michał Fabisiak , Jan Peszek

This paper is concerned with the Fokker-Planck (FP) description of classical stochastic systems with discrete time delay. The non-Markovian character of the corresponding Langevin dynamics naturally leads to a coupled infinite hierarchy of…

Statistical Mechanics · Physics 2018-07-03 Sarah A. M. Loos , Sabine H. L. Klapp

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…

Optimization and Control · Mathematics 2026-01-21 Zongxia Liang , Zhou Zhou , Yaqi Zhuang , Bin Zou

The mean-field limit of systems of rank-based interacting diffusions is known to be described by a nonlinear diffusion process. We obtain a similar description at the level of stationary distributions. Our proof is based on explicit…

Probability · Mathematics 2015-01-21 Julien Reygner

Incorporating social interactions is essential to an accurate modeling of epidemic spreading. This work proposes a novel local mean-field density functional theory model by using the sum-of-exponential approximation of convolution kernels…

Physics and Society · Physics 2025-09-09 Ziheng Xu , Shenggao Zhou

The derivation of effective descriptions for interacting many-body systems is an important branch of applied mathematics. We prove a propagation of chaos result for a system of $N$ particles subject to Newtonian time evolution with or…

Mathematical Physics · Physics 2025-05-20 Li Chen , Jinwook Jung , Peter Pickl , Zhenfu Wang

Recent research has been focused on two different approaches to studying neural networks training in the limit of infinite width (1) a mean-field (MF) and (2) a constant neural tangent kernel (NTK) approximations. These two approaches have…

Machine Learning · Computer Science 2020-10-23 Eugene A. Golikov

We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence…

Optimization and Control · Mathematics 2017-10-04 Christoforos Somarakis , Evripidis Paraskevas , John S. Baras , Nader Motee

We consider a stochastic, continuous state and time opinion model where each agent's opinion locally interacts with other agents' opinions in the system, and there is also exogenous randomness. The interaction tends to create clusters of…

Social and Information Networks · Computer Science 2016-02-29 Josselin Garnier , George Papanicolaou , Tzu-Wei Yang

A one-dimensional rule-based model for flocking, that combines velocity alignment and long-range centering interactions, is presented and studied. The induced cohesion in the collective motion of the self-propelled agents leads to a unique…

Statistical Mechanics · Physics 2015-01-19 V. Dossetti

The problem of reservation in a large distributed system is analyzed via a new mathematical model. A typical application is a station-based car-sharing system which can be described as a closed stochastic network where the nodes are the…

Probability · Mathematics 2024-10-01 Christine Fricker , Hanene Mohamed

The paper focuses on mean-field type multi-agent control problems with finite state and action spaces where the dynamics and cost structures are symmetric and homogeneous, and are affected by the distribution of the agents. A standard…

Optimization and Control · Mathematics 2025-07-03 Erhan Bayraktar , Ali D. Kara

We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…

Analysis of PDEs · Mathematics 2020-03-10 Y Achdou , Z Kobeissi

In this work we study propagation of chaos for solutions of the Liouville equation for the classical discrete Cucker-Smale system. Assuming that the communication kernel satisfies the heavy tail condition -- known to be necessary to induce…

Analysis of PDEs · Mathematics 2021-12-09 Vinh Nguyen , Roman Shvydkoy