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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 develop a limit theory for controlled mean field stochastic partial differential equations in a variational framework. More precisely, we prove existence results for mean field limits and particle approximations, and we establish a…

Probability · Mathematics 2026-05-20 David Criens

We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a…

Mathematical Physics · Physics 2009-11-13 J. Froehlich , A. Knowles , E. Lenzmann

Generalized hydrodynamic theory, which does not rest on the requirement of a local equilibrium, is derived in the long-wave limit of a kinetic equation. The theory bridges the whole frequency range between the quasistatic (Navier-Stokes)…

Soft Condensed Matter · Physics 2009-10-31 I. V. Tokatly , O. Pankratov

We present a unified framework, with quantitative estimates, for deterministic interacting particle systems whose pairwise interactions may depend on heterogeneous labels. Heterogeneity is kept at every level by adding a frozen label…

Analysis of PDEs · Mathematics 2026-05-21 Thierry Paul , Emmanuel Trélat

We establish a quantitfied overdamped limit for kinetic Vlasov-Fokker-Planck equations with nonlocal interaction forces. We provide explicit bounds on the error between solutions of that kinetic equation and the limiting equation, which is…

Analysis of PDEs · Mathematics 2021-06-01 Young-Pil Choi , Oliver Tse

This paper is concerned with the incompressible limit of the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions in R^N(N = 2, 3). It is rigorously shown that the local (and global) strong solution of the…

Analysis of PDEs · Mathematics 2014-05-06 Shijin Ding , Jinrui Huang , Huanyao Wen , Ruizhao Zi

Exact expressions are derived for the pair and three-body hydrodynamic interactions between a sphere and a number of small particles immersed in a viscous incompressible fluid. The analysis is based on the Stokes equations of low Reynolds…

Fluid Dynamics · Physics 2015-06-22 Maria L. Ekiel-Jezewska , B. U. Felderhof

We consider dynamics of the empirical measure of vertex neighborhood states of Markov interacting jump processes on sparse random graphs, in a suitable asymptotic limit as the graph size goes to infinity. Under the assumption of a certain…

Probability · Mathematics 2025-02-10 Juniper Cocomello , Michel Davydov , Kavita Ramanan

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

We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and…

Disordered Systems and Neural Networks · Physics 2009-11-07 Francesco Guerra , Fabio L. Toninelli

We study the hydrodynamic limit of the Chern--Simons--Higgs system, a relativistic gauge field model involving the Chern--Simons interaction. We introduce a single scaling parameter capturing both the non-relativistic (infinite speed of…

Analysis of PDEs · Mathematics 2026-04-10 Jeongho Kim , Bora Moon

We consider a system of hierarchical interacting spins under dynamics of spin-flip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical…

Probability · Mathematics 2019-10-31 Paolo Dai Pra , Marco Formentin , Guglielmo Pelino

We consider an Individual-Based Model for self-rotating particles interacting through local alignment and investigate its macroscopic limit. This model describes self-propelled particles moving in the plane and trying to synchronize their…

Mathematical Physics · Physics 2013-06-17 Pierre Degond , Giacomo Dimarco , Thi Bich Ngoc Mac

We establish the mean-field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-coulombic Riesz potential, for the first time in arbitrary…

Analysis of PDEs · Mathematics 2020-12-23 Sylvia Serfaty , appendix with Mitia Duerinckx

We study the hydrodynamic limit for three gradient spin models: generalized Kipnis-Marchioro-Presutti (KMP), its discrete version and a family of harmonic models, under symmetric and nearest-neighbor interactions. These three models share…

Probability · Mathematics 2025-05-19 Chiara Franceschini , Patrícia Gonçalves , Kohei Hayashi , Makiko Sasada

In this paper a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method. The model under investigation is an interacting particle system coupled to the eikonal equation…

Analysis of PDEs · Mathematics 2016-11-28 Li Chen , Simone Göttlich , Qitao Yin

The existence of the thermodynamic limit in spin systems with short- and long-range interactions is established. We consider the infinite-volume limit with a fixed shape of the system. The variational expressions of the entropy density and…

Statistical Mechanics · Physics 2015-03-18 Takashi Mori

The stochastic limit for the system of spins interacting with a boson field is investigated. In the finite volume an application of the stochastic golden rule shows that in the limit the dynamics of a quantum system is described by a…

Quantum Physics · Physics 2009-10-31 L. Accardi , S. V. Kozyrev

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