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Related papers: Mean-Field Limits for Stochastic Interacting Parti…

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In this paper we intend to present a unified treatment of a variety of singular interacting particle systems and their McKean-Vlasov limits. This unified approach is based on the use of the relative entropy on the path space in the spirit…

Analysis of PDEs · Mathematics 2024-12-11 Patrick Cattiaux

This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and…

Computational Physics · Physics 2025-05-29 Shiba Biswal , Karthik Elamvazhuthi , Rishi Sonthalia

This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…

Methodology · Statistics 2021-04-28 Daniel Sanz-Alonso , Ruiyi Yang

Rich out of equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular or colloidal systems,…

Statistical Mechanics · Physics 2023-05-03 Leticia F. Cugliandolo

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

Probability · Mathematics 2025-06-09 Pascal Bianchi , Walid Hachem , Victor Priser

This paper establishes an indirect approximation theorem for the most probable transition pathway of a stochastic interacting particle system in the mean-field framework. This paper studied the problem of indirect approximation of the most…

Dynamical Systems · Mathematics 2026-05-27 Jianyu Chen , Ting Gao , Galina Strelkova , Jinqiao Duan

We study the problem of parameter estimation for large exchangeable interacting particle systems when a sample of discrete observations from a single particle is known. We propose a novel method based on martingale estimating functions…

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

Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We…

Probability · Mathematics 2020-03-19 Tibor Mach , Anja Sturm , Jan M. Swart

This review is devoted to generalization of dynamical mean-field theory (DMFT) for strongly correlated electronic systems towards the account of different types of additional interactions, necessary for correct physical description of many…

Strongly Correlated Electrons · Physics 2015-05-30 E. Z. Kuchinskii , I. A. Nekrasov , M. V. Sadovskii

Hypergraphs effectively model higher-order relationships in natural phenomena, capturing complex interactions beyond pairwise connections. We introduce a novel hypergraph message passing framework inspired by interacting particle systems,…

Machine Learning · Computer Science 2025-05-27 Yixuan Ma , Kai Yi , Pietro Lio , Shi Jin , Yu Guang Wang

Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…

Methodology · Statistics 2017-11-08 Philipp Frank , Theo Steininger , Torsten A. Enßlin

In this work, we investigate the mean-field limit of a model consisting in $m \geq 1 $ tracer particles, coupled to an interacting boson field. We assume the mass of the tracer particles and the expected number of bosons to be of the same…

Mathematical Physics · Physics 2021-08-18 Esteban Cárdenas

We study the mean-field limit of a generic class of dynamic co-evolving latent space networks motivated by the social and opinion dynamics literature. Such models include $n$ agents, whose opinions are given by latent stochastic processes,…

Probability · Mathematics 2026-04-24 Ankan Ganguly , Konstantinos Spiliopoulos , Daniel Sussman

We consider a particle system with uniform coupling between a macroscopic component and individual particles. The constraint for each particle is of full rank, which implies that each movement of the macroscopic component leads to a…

Analysis of PDEs · Mathematics 2022-03-15 Steffen Plunder , Bernd Simeon

Dynamical mean-field theory (DMFT) is a non-perturbative technique for the investigation of correlated electron systems. Its combination with the local density approximation (LDA) has recently led to a material-specific computational scheme…

Strongly Correlated Electrons · Physics 2009-11-10 D. Vollhardt , K. Held , G. Keller , R. Bulla , Th. Pruschke , I. A. Nekrasov , V. I. Anisimov

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

We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution…

Probability · Mathematics 2021-07-19 Erhan Bayraktar , Ruoyu Wu

We consider interacting agent systems with a large number of stochastic agents (or particles) influenced by a fixed number of external stochastic lead agents. Such examples arise, for example in models of opinion dynamics, where a small…

Optimization and Control · Mathematics 2025-12-23 Sebastian Zimper , Ana Djurdjevac , Carsten Hartmann , Christof Schütte , Nataša Djurdjevac Conrad

The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…

Quantitative Methods · Quantitative Biology 2024-07-16 Eric Medwedeff , Eric Mjolsness

A model is developed with the aim of analyzing interacting superparamagnets. Model is built from magnetic dipolar interaction and demagnetizing mean field concepts. A useful expression for effective demagnetizing factors is achieved, which…

Mesoscale and Nanoscale Physics · Physics 2017-04-19 F. H. Sánchez , P. Mendoza Zélis , M. L. Arciniegas , G. A. Pasquevich , M. B. Fernández van Raap