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We consider particle-based stochastic reaction-drift-diffusion models where particles move via diffusion and drift induced by one- and two-body potential interactions. The dynamics of the particles are formulated as measure-valued…

Probability · Mathematics 2025-01-22 Max Heldman , Samuel A. Isaacson , Qianhan Liu , Konstantinos Spiliopoulos

In this paper we derive a two dimensional spray model with gyroscopic effects as the mean-field limit of a system modeling the interaction between an incompressible fluid and a finite number of solid particles. This spray model has been…

Analysis of PDEs · Mathematics 2023-07-11 Matthieu Ménard

We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as…

Probability · Mathematics 2022-10-07 Erhan Bayraktar , Suman Chakraborty , Ruoyu Wu

We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random…

Probability · Mathematics 2020-11-24 Xavier Erny , Eva Löcherbach , Dasha Loukianova

This paper establishes a non-uniform Berry--Esseen bound in normal approximation for exchangeable pairs using Stein's method via a concentration inequality approach. The main theorem extends and improves several results in the literature,…

Probability · Mathematics 2025-02-18 Lê Vǎn Thành , Nguyen Ngoc Tu

We study the problem of reconstructing interaction kernels in systems of interacting agents from macroscopic measurements when posed as an optimization problem. The reconstruction procedure depends on the formulation of the forward model,…

Numerical Analysis · Mathematics 2026-04-03 Peiyi Chen , Qin Li , Li Wang , Yunan Yang

The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence…

Analysis of PDEs · Mathematics 2024-06-19 Li Chen , Paul Nikolaev , David J. Prömel

We consider a class of weakly interacting particle systems of mean-field type. The interactions between the particles are encoded in a graph sequence, i.e., two particles are interacting if and only if they are connected in the underlying…

Probability · Mathematics 2023-07-06 Gianmarco Bet , Fabio Coppini , Francesca R. Nardi

We introduce a new approach to derive mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to…

Analysis of PDEs · Mathematics 2025-02-12 Didier Bresch , Mitia Duerinckx , Pierre-Emmanuel Jabin

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

We consider large systems of particles interacting through rough but bounded interaction kernels. We are able to control the relative entropy between the $N$-particle distribution and the expected limit which solves the corresponding Vlasov…

Analysis of PDEs · Mathematics 2015-11-13 Pierre-Emmanuel Jabin , Zhenfu Wang

The problem of non--interacting electrons on a square lattice subject to a random magnetic flux is mapped onto a one--dimensional model with infinitely many orbitals per site. Linking each orbital with $N(\gg1)$ other orbitals maps the…

Condensed Matter · Physics 2007-05-23 B. Kramer , D. Belitz , M. Batsch

The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations.…

Analysis of PDEs · Mathematics 2019-09-04 Li Chen , Esther S. Daus , Ansgar Jüngel

The mean-field limit for the dynamics of bosons with random interactions is rigorously studied. It is shown that, for interactions that are almost-surely bounded, the many-body quantum evolution can be replaced in the mean-field limit by a…

Mathematical Physics · Physics 2009-11-13 Walid K. Abou Salem

Many natural phenomena are effectively described by interacting particle systems, which can be modeled using either deterministic or stochastic differential equations (SDEs). In this study, we specifically investigate particle systems…

Analysis of PDEs · Mathematics 2024-04-01 Christian Kuehn , Carlos Pulido

We report on a simple strategy to treat mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. Extending the method of counting, introduced in [Lett. Math.…

Mathematical Physics · Physics 2021-04-27 Nikolai Leopold , Peter Pickl

The mean-field reaction-diffusion equations of the diffusive pair-annihilation and triplett-annihilation processes are considered. A direct lower bound on the time-dependent mean particle-density is derived. The results are applied to the…

Mathematical Physics · Physics 2007-05-23 Malte Henkel

This paper considers an $n$-particle jump-diffusion system with mean filed interaction, where the coefficients are locally Lipschitz continuous. We address the convergence as $n\to\infty$ of the empirical measure of the jump-diffusions to…

Probability · Mathematics 2024-02-27 Zeqian Li

Motivated by an application to empirical Bayes learning in high-dimensional regression, we study a class of Langevin diffusions in a system with random disorder, where the drift coefficient is driven by a parameter that continuously adapts…

Statistics Theory · Mathematics 2025-11-04 Zhou Fan , Justin Ko , Bruno Loureiro , Yue M. Lu , Yandi Shen

This paper develops a non-asymptotic approach to mean field approximations for systems of $n$ diffusive particles interacting pairwise. The interaction strengths are not identical, making the particle system non-exchangeable. The marginal…

Probability · Mathematics 2026-04-17 Daniel Lacker , Lane Chun Yeung , Fuzhong Zhou