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We present a construction of a mean-field theory for thermodynamic and spectral properties of correlated electrons reliable in the strong-coupling limit. We introduce an effective interaction determined self-consistently from the reduced…

Strongly Correlated Electrons · Physics 2017-04-19 Václav Janiš , Vladislav Pokorný , Anna Kauch

The diffraction patterns of crystalline materials with strongly-correlated disorder are characterised by the presence of structured diffuse scattering. Conventional analysis approaches generally seek to interpret this scattering either…

Disordered Systems and Neural Networks · Physics 2021-07-29 Ella M. Schmidt , Johnathan M. Bulled , Andrew L. Goodwin

This paper delves into a nonparametric estimation approach for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an…

Statistics Theory · Mathematics 2024-02-23 Denis Belomestny , Mark Podolskij , Shi-Yuan Zhou

Calculations of two-particle correlations usually assume particles interact only pair-wise after their final collisions with third bodies. By considering classical trajectories, we show that interactions with the mean field can alter the…

Nuclear Theory · Physics 2009-11-11 Scott Pratt

Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional…

Disordered Systems and Neural Networks · Physics 2009-10-31 J. Houdayer , J. H. Boutet de Monvel , O. C. Martin

Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples --…

Machine Learning · Statistics 2026-05-15 Ayoub Belhadji , Daniel Sharp , Youssef M. Marzouk

We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…

Probability · Mathematics 2020-06-02 Carsten Chong , Claudia Klüppelberg

We present an analytic calculation of the layer (parallel) susceptibility at the extraordinary transition in a semi-infinite system with a flat boundary. Using the method of integral transforms put forward by McAvity and Osborn [Nucl. Phys.…

High Energy Physics - Theory · Physics 2021-01-15 M. A. Shpot

Inspired by the works in [1] and [8] we introduce what we call $k$-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This…

Probability · Mathematics 2020-04-21 Mario Ayala , Gioia Carinci , Frank Redig

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

In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…

Dynamical Systems · Mathematics 2025-06-25 Zheng Bian , Jeroen S. W. Lamb , Tiago Pereira

We explore quantum correlations of general vector-light fields in multislit interference and show that the $n$th-order field-coherence matrix is directly linked with the reduced $n$-photon density matrix. The connection is utilized to…

Quantum Physics · Physics 2019-04-17 Andreas Norrman , Łukasz Rudnicki

Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…

Neurons and Cognition · Quantitative Biology 2022-06-10 Giancarlo La Camera

Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and give rise to a variety of…

Mathematical Physics · Physics 2018-07-27 Sylvia Serfaty

These notes are devoted to a summary on the mean-field limit of large ensembles of interacting particles with applications in swarming models. We first make a summary of the kinetic models derived as continuum versions of second order…

Analysis of PDEs · Mathematics 2015-06-15 J. A. Carrillo , Y. -P. Choi , M. Hauray

The mean field approximation to the Ising model is a canonical variational tool that is used for analysis and inference in Ising models. We provide a simple and optimal bound for the KL error of the mean field approximation for Ising models…

Machine Learning · Computer Science 2018-02-22 Vishesh Jain , Frederic Koehler , Elchanan Mossel

We consider an interacting system of one-dimensional structures modelling fibers with fiber-fiber interaction in a fiber lay-down process. The resulting microscopic system is investigated by looking at different asymptotic limits of the…

Dynamical Systems · Mathematics 2017-10-06 Raul Borsche , Axel Klar , Christian Nessler , Andreas Roth , Oliver Tse

We introduce a well-defined and unbiased measure of the strength of correlations in quantum many-particle systems which is based on the relative von Neumann entropy computed from the density operator of correlated and uncorrelated states.…

Strongly Correlated Electrons · Physics 2015-05-30 K. Byczuk , J. Kunes , W. Hofstetter , D. Vollhardt

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 study a leader-follower system of interacting particles subject to feedback control and derive its mean-field limits through a two-step passage: first to a micro-macro system coupling leader particles with a follower fluid, and then to a…

Analysis of PDEs · Mathematics 2025-08-07 Giacomo Albi , Young-Pil Choi , Matteo Piu , Sihyun Song