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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

We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…

Probability · Mathematics 2022-04-19 Alexander Stolyar

This article is concerned with moderate deviation principles of a general class of mean eld type interacting particle models. We discuss functional moderate deviations of the occupation measures for both the strong -topology on the space of…

Probability · Mathematics 2012-04-17 Pierre Del Moral , Shulan Hu , Liming Wu

In this work, we consider one-dimensional particles interacting in mean-field type through a bounded kernel. In addition, when particles hit some barrier (say zero), they are removed from the system. This absorption of particles is…

Probability · Mathematics 2026-04-07 Gaoyue Guo , Maxime Latypov , Milica Tomasevic

We study the convergence problem of mean-field control theory in the presence of state constraints and non-degenerate idiosyncratic noise. Our main result is the convergence of the value functions associated to stochastic control problems…

Optimization and Control · Mathematics 2023-06-02 Samuel Daudin

This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the…

Analysis of PDEs · Mathematics 2020-11-17 Didier Bresch , Pierre-Emmanuel Jabin , Zhenfu Wang

We develop a continuum limit and mean-field theory for interacting particle systems (IPS) on self-similar networks, a new class of discrete models whose large-scale behavior gives rise to nonlocal evolution equations on fractal domains.…

Dynamical Systems · Mathematics 2026-02-02 Georgi S. Medvedev

When spatial correlations are short-range, the physics of strongly correlated systems is controlled by local quantum fluctuations. In those regimes, Dynamical Mean-Field Theory can be viewed as a `compass' which provides guidance on the…

Strongly Correlated Electrons · Physics 2015-06-03 Antoine Georges

Given an arbitrary finite dimensional Hamiltonian H_0, we consider the model H=H_0+\Delta H, where \Delta H is a generic fully connected interaction. By using the strong law of large numbers we easily prove that, for all such models, a…

Statistical Mechanics · Physics 2012-03-19 M. Ostilli

We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…

Probability · Mathematics 2015-05-14 Francesca Collet , Paolo Dai Pra , Elena Sartori

Assuming that the effect of the residual interaction beyond mean-field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of Markovian quantum jump are presented. A simplified…

Quantum Physics · Physics 2009-11-11 Denis Lacroix

Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…

Statistical Mechanics · Physics 2009-10-31 Peter J. Klinko , Bruce N. Miller

Two-particle rapidity (or pseudorapidity) correlation function $C(y_1, y_2)$ was used in analysing fluctuation of particle density distribution in rapidity in high-energy heavy-ion collisions. In our research, we argue that for a centrality…

Nuclear Theory · Physics 2017-05-22 Ronghua He , Jing Qian , Lei Huo

We extend a recent billiard model of the nuclear N-body Hamiltonian to consider a finite two-body interaction. This permits a treatment of the Hamiltonian by a mean field theory, and also allows the possibility to model reactions between…

Nuclear Theory · Physics 2009-10-31 George F. Bertsch , Thomas Papenbrock , Sanjay Reddy

We consider cooperative reactions and we study the effects of the interaction strength among the system components on the reaction rate, hence realizing a connection between microscopic and macroscopic observables. Our approach is based on…

Quantitative Methods · Quantitative Biology 2012-06-07 Aldo Di Biasio , Elena Agliari , Adriano Barra , Raffaella Burioni

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 consider a system of diffusing particles on the real line in a quadratic external potential and with repulsive electrostatic interaction. The empirical measure process is known to converge weakly to a deterministic measure-valued process…

Probability · Mathematics 2010-03-23 Martin Bender

We consider a $N$-particle interacting particle system with the vision geometrical constraints and reflected noises, proposed as a model for collective behavior of individuals. We rigorously derive a continuity-type of mean-field equation…

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

A general self-consistency approach allows a thorough treatment of the corrections to the standard mean-field approximation (MFA). The natural extension of standard MFA with the help of a cumulant expansion leads to a new point of view on…

Statistical Mechanics · Physics 2007-05-23 Dimo I. Uzunov

We consider fluctuations in the distribution of critical points - saddle points, minima and maxima - of random gaussian fields. We calculate the asymptotic limits of the two point correlation function for various critical point densities,…

Disordered Systems and Neural Networks · Physics 2011-12-12 Avraham Klein , Oded Agam