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In this paper, we consider graphon particle systems with heterogeneous mean-field type interactions and the associated finite particle approximations. Under suitable growth (resp. convexity) assumptions, we obtain uniform-in-time…

Probability · Mathematics 2022-10-21 Erhan Bayraktar , Ruoyu Wu

We consider thermodynamically consistent autonomous Markov jump processes displaying a macroscopic limit in which the logarithm of the probability distribution is proportional to a scale-independent rate function (i.e., a large deviations…

Statistical Mechanics · Physics 2021-09-22 Nahuel Freitas , Gianmaria Falasco , Massimiliano Esposito

For finite size Markov chains, the Donsker-Varadhan theory fully describes the large deviations of the time averaged empirical measure. We are interested in the extension of the Donsker-Varadhan theory for a large size non-equilibrium…

Probability · Mathematics 2024-05-06 Thierry Bodineau , Benoit Dagallier

A particle system is said to be non-exchangeable if two particles cannot be exchanged without modifying the overall dynamics. Because of this property, the classical mean-field approach fails to provide a limit equation when the number of…

Analysis of PDEs · Mathematics 2024-01-17 Nathalie Ayi , Nastassia Pouradier Duteil

Correlated quantum systems feature a wide range of nontrivial effects emerging from interactions between their constituting particles. In nonequilibrium scenarios, these manifest in phenomena such as many-body insulating states and…

Quantum Physics · Physics 2024-03-11 Juan José Mendoza-Arenas , Stephen R. Clark

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 study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…

Statistical Mechanics · Physics 2015-01-20 Naoto Shiraishi

This article examines large time behaviour of finite state mean-field interacting particle systems. Our first main result is a sharp estimate (in the exponential scale) on the time required for convergence of the empirical measure process…

Probability · Mathematics 2021-03-02 Sarath Yasodharan , Rajesh Sundaresan

The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route…

Probability · Mathematics 2009-12-15 Carl Graham , Philippe Robert

Following Kolokoltsov's work [1], we present an extension of mean-field control theory in quantum framework. In particular such an extension is done naturally by considering the Belavkin quantum filtering and control theory in a mean-field…

Optimization and Control · Mathematics 2023-06-27 Sofiane Chalal , Nina H. Amini , Gaoyue Guo

This paper develops a statistical framework for goodness-of-fit testing of volatility functions in McKean-Vlasov stochastic differential equations, which describe large systems of interacting particles with distribution-dependent dynamics.…

Methodology · Statistics 2025-10-15 Akram Heidari , Mark Podolskij

Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…

Mesoscale and Nanoscale Physics · Physics 2021-08-04 David T. Limmer , Chloe Y. Gao , Anthony R. Poggioli

A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a…

Analysis of PDEs · Mathematics 2021-09-20 Li Chen , Alexandra Holzinger , Ansgar Jüngel , Nicola Zamponi

Active systems, which are driven out of equilibrium by local non-conservative forces, exhibit unique behaviors and structures with potential utility for the design of novel materials. An important and difficult challenge along the path…

Soft Condensed Matter · Physics 2022-08-09 Laura Tociu , Gregory Rassolov , Étienne Fodor , Suriyanarayanan Vaikuntanathan

Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their…

Disordered Systems and Neural Networks · Physics 2018-11-20 Elisabeth Agoritsas , Giulio Biroli , Pierfrancesco Urbani , Francesco Zamponi

We analyze a class of nonlinear partial differential equations (PDEs) defined on $\mathbb{R}^d \times \mathcal{P}_2(\mathbb{R}^d),$ where $\mathcal{P}_2(\mathbb{R}^d)$ is the Wasserstein space of probability measures on $\mathbb{R}^d$ with…

Probability · Mathematics 2015-04-23 Jean-François Chassagneux , Dan Crisan , François Delarue

We study the discrete Fokker-Planck equation associated with the mean-field dynamics of a particle system called the dispersion process. For different regimes of the average number of particles per site (denoted by $\mu > 0$), we establish…

Probability · Mathematics 2025-08-25 Fei Cao , Jincheng Yang

Stochastic interacting particle systems are widely used to model collective phenomena across diverse fields, including statistical physics, biology, and social dynamics. The McKean-Vlasov equation arises as the mean-field limit of such…

Computational Physics · Physics 2025-09-17 Zhiqiang Cai , Chengyu Liu , Xiang Zhou

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such…

Mathematical Physics · Physics 2019-06-28 Noé Cuneo , Vojkan Jakšić , Claude-Alain Pillet , Armen Shirikyan

We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: it has the same weak limit as…

Probability · Mathematics 2026-03-24 Nikolaos Kolliopoulos , Martin Larsson , Zeyu Zhang