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The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set of assumptions. Under further assumptions on the evolution…

Analysis of PDEs · Mathematics 2022-10-04 Stefano Almi , Claudio D'Eramo , Marco Morandotti , Francesco Solombrino

We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod…

Probability · Mathematics 2009-09-29 Sourav Chatterjee

We study the random-field Ising model with long-range interactions and show the exactness of the mean-field theory under certain mild conditions. This is a generalization of the result of Mori for the non-random and spin-glass cases. To…

Statistical Mechanics · Physics 2015-06-18 Junichi Tsuda , Hidetoshi Nishimori

The cluster mean-field approximations are performed, up to 13 cluster sizes, to study the critical behavior of the driven pair contact process with diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points are…

Statistical Mechanics · Physics 2007-05-23 Su-Chan Park , Hyunggyu Park

The success of the "Cluster Variation Method" (CVM) in reproducing quite accurately the free energies of Monte Carlo (MC) calculations on Ising models is explained in terms of identifying a cancellation of errors: We show that the CVM…

Materials Science · Physics 2009-10-31 Luiz G. Ferreira , C. Wolverton , Alex Zunger

We propose a novel approach to the inverse Ising problem which employs the recently introduced Density Consistency approximation (DC) to determine the model parameters (couplings and external fields) maximizing the likelihood of given…

Statistical Mechanics · Physics 2021-04-01 Alfredo Braunstein , Giovanni Catania , Luca Dall'Asta , Anna Paola Muntoni

We investigate the mean-field limit for interacting particle systems through a duality-based framework and obtain quantitative estimates on the convergence of marginals as well as on correlation functions. In particular, for merely…

Analysis of PDEs · Mathematics 2026-05-05 Nadia Khoury , P. -E. Jabin

In the present paper we show how non--classical, quite accurate, critical exponents can be extracted in a very simple way from the Pad\'e analysis of the results obtained by mean field like approximation schemes, and in particular by the…

Condensed Matter · Physics 2009-10-22 A. Pelizzola

Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…

Artificial Intelligence · Computer Science 2012-05-14 Ido Cohn , Tal El-Hay , Nir Friedman , Raz Kupferman

We develop an advanced mean field method for approximating averages in probabilistic data models that is based on the TAP approach of disorder physics. In contrast to conventional TAP, where the knowledge of the distribution of couplings…

Disordered Systems and Neural Networks · Physics 2009-11-07 Manfred Opper , Ole Winther

We show that model-based Bayesian clustering, the probabilistically most systematic approach to the partitioning of data, can be mapped into a statistical physics problem for a gas of particles, and as a result becomes amenable to a…

Disordered Systems and Neural Networks · Physics 2018-10-24 Alexander Mozeika , Anthony CC Coolen

This paper concerns the nonparametric estimation problem of the distribution-state dependent drift vector field in an interacting $N$-particle system. Observing single-trajectory data for each particle, we derive the mean-field rate of…

Statistics Theory · Mathematics 2022-06-28 Rentian Yao , Xiaohui Chen , Yun Yang

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

For a certain class of McKean-Vlasov processes, we introduce proxy processes that substitute the mean-field interaction with self-interaction, employing a weighted occupation measure. Our study encompasses two key achievements. First, we…

Probability · Mathematics 2025-11-04 Kai Du , Zhenjie Ren , Florin Suciu , Songbo Wang

We use the mean-field approximation to simplify the master equation for sympathetic cooling of Bosons. For the mean single-particle occupation numbers, this approach yields the same equations as the factorization assumption introduced in an…

Condensed Matter · Physics 2009-11-07 S. J. Wang , M. C. Nemes , A. N. Salgueiro , H. A. Weidenmueller

The free energy is a key quantity of interest in Ising models, but unfortunately, computing it in general is computationally intractable. Two popular (variational) approximation schemes for estimating the free energy of general Ising models…

Machine Learning · Computer Science 2018-08-30 Vishesh Jain , Frederic Koehler , Andrej Risteski

The scaling behavior of the entanglement entropy in the two-dimensional random transverse field Ising model is studied numerically through the strong disordered renormalization group method. We find that the leading term of the entanglement…

Disordered Systems and Neural Networks · Physics 2009-11-13 Rong Yu , Hubert Saleur , Stephan Haas

A novel mean-field approximation for quasi-one-dimensional (Q1D) quantum magnets is formulated. Our new mean-field approach is based on the Bethe-type effective-field theory, where thermal and quantum fluctuations between the…

Strongly Correlated Electrons · Physics 2008-12-12 Synge Todo , Akira Shibasaki

The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the…

Optimization and Control · Mathematics 2026-02-16 Hui Huang , Jethro Warnett

Making statistical predictions requires tackling two problems: one must assign appropriate probability distributions and then one must calculate a variety of expected values. The method of maximum entropy is commonly used to address the…

Statistical Mechanics · Physics 2009-11-07 Chih-Yuan Tseng , Ariel Caticha