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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

We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…

Biological Physics · Physics 2017-11-22 Farzad Farkhooi , Wilhelm Stannat

In some systems, the behavior of the constituent units can create a `context' that modifies the direct interactions among them. This mechanism of indirect modification inspired us to develop a minimal model of context-dependent spreading.…

Physics and Society · Physics 2023-06-13 Giulio Burgio , Sergio Gómez , Alex Arenas

We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…

Probability · Mathematics 2009-02-16 Charles Bordenave , David McDonald , Alexandre Proutiere

Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered…

Systems and Control · Electrical Eng. & Systems 2023-12-12 Christian Fiedler , Michael Herty , Sebastian Trimpe

Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent…

Probability · Mathematics 2022-11-22 François Baccelli , Michel Davydov , Thibaud Taillefumier

We consider a network of randomly coupled rate-based neurons influenced by external and internal noise. We derive a second-order stochastic mean-field model for the network dynamics and use it to analyze the stability and bifurcations in…

Chaotic Dynamics · Physics 2015-12-14 Vladimir Klinshov , Igor Franovic

I study peer effects that arise from irreversible decisions in the absence of a standard social equilibrium. I model a latent sequence of decisions in continuous time and obtain a closed-form expression for the likelihood, which allows to…

Econometrics · Economics 2026-02-18 Vincent Starck

In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…

Probability · Mathematics 2017-01-05 Tanguy Cabana , Jonathan Touboul

A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population.…

Optimization and Control · Mathematics 2021-06-15 Giacomo Albi , Stefano Almi , Marco Morandotti , Francesco Solombrino

The brain's activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable…

Dynamical Systems · Mathematics 2012-11-07 Jonathan Touboul , G. Bard Ermentrout

In this paper, we derive the mean-field limit of a collective dynamics model with time-varying weights, for weight dynamics that preserve the total mass of the system as well as indistinguishability of the agents. The limit equation is a…

Analysis of PDEs · Mathematics 2021-03-12 Nastassia Pouradier Duteil

We investigate reinforcement learning in the setting of Markov decision processes for a large number of exchangeable agents interacting in a mean field manner. Applications include, for example, the control of a large number of robots…

Optimization and Control · Mathematics 2025-04-30 René Carmona , Mathieu Laurière , Zongjun Tan

We develop original models to study interacting agents in financial markets and in social networks. Within these models randomness is vital as a form of shock or news that decays with time. Agents learn from their observations and learning…

Mathematical Finance · Quantitative Finance 2023-07-14 Ionel Popescu , Tushar Vaidya

An abstract network approach is proposed for the description of the dynamics in reactive processes. The phase space of the variables (concentrations in reactive systems) is partitioned into a finite number of segments, which constitute the…

Statistical Mechanics · Physics 2015-06-17 A. Provata , E. Panagakou

Over the past two decades, there has been a tremendous increase in the growth of representation learning methods for graphs, with numerous applications across various fields, including bioinformatics, chemistry, and the social sciences.…

Machine Learning · Computer Science 2023-12-21 Abdulkadir Celikkanat , Nikolaos Nakis , Morten Mørup

Consider the class of Ensemble Square Root filtering algorithms for the numerical approximation of the posterior distribution of nonlinear Markovian signals partially observed with linear observations corrupted with independent measurement…

Probability · Mathematics 2021-02-01 Theresa Lange , Wilhelm Stannat

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

Many real-world phenomena can be modelled as dynamical processes on networks, a prominent example being the spread of infectious diseases such as COVID-19. Mean-field approximations are a widely used tool to analyse such dynamical processes…

Probability · Mathematics 2025-08-25 Jonathan A. Ward , Gábor Timár , Péter L. Simon

A class of dynamic threshold models is proposed, for describing the upset of collective actions in social networks. The agents of the network have to decide whether to undertake a certain action or not. They make their decision by comparing…

Social and Information Networks · Computer Science 2016-05-23 Andrea Garulli , Antonio Giannitrapani