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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

Many natural phenomena are effectively described by interacting particle systems, which can be modeled using either deterministic or stochastic differential equations (SDEs). In this study, we specifically investigate particle systems…

Analysis of PDEs · Mathematics 2024-04-01 Christian Kuehn , Carlos Pulido

We propose an approach to modelling large-scale multi-agent dynamical systems allowing interactions among more than just pairs of agents using the theory of mean field games and the notion of hypergraphons, which are obtained as limits of…

Computer Science and Game Theory · Computer Science 2022-11-23 Kai Cui , Wasiur R. KhudaBukhsh , Heinz Koeppl

We introduce and study a nonlinear discrete dynamical system describing the evolution of a resource distribution among interacting agents. The model generalizes several classical mean-field and opinion-dynamics frameworks and is defined on…

Dynamical Systems · Mathematics 2026-04-28 Oksana Satur

We introduce the concept of {\it mean-field optimal control} which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional…

Optimization and Control · Mathematics 2019-02-20 Massimo Fornasier , Francesco Solombrino

The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…

Dynamical Systems · Mathematics 2024-08-06 Christian Bick , Davide Sclosa

In this paper we propose a framework to investigate the mean field limit (MFL) of interacting particle systems on directed hypergraphs. We provide a non-trivial measure-theoretic viewpoint and make extensions of directed hypergraphs as…

Analysis of PDEs · Mathematics 2025-02-18 Christian Kuehn , Chuang Xu

We establish mean-field limits for large-scale random-access networks with buffer dynamics and arbitrary interference graphs. While saturated-buffer scenarios have been widely investigated and yield useful throughput estimates for…

Probability · Mathematics 2019-04-25 Fabio Cecchi , Sem C. Borst , Johan S. H. van Leeuwaarden , Philip A. Whiting

This paper considers the distributed consensus problem of multi-agent systems with general continuous-time linear dynamics. Two distributed adaptive dynamic consensus protocols are proposed, based on the relative output information of…

Systems and Control · Computer Science 2015-01-20 Zhongkui Li , Xiangdong Liu , Wei Ren , Lihua Xie

We give a general existence and convergence result for interacting particle systems on locally finite graphs with possibly unbounded degrees or jump rates. We allow the local state space to be Polish, and the jumps at a site to affect the…

Probability · Mathematics 2026-01-15 Kuldeep Guha Mazumder

We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…

Probability · Mathematics 2011-10-25 A. Manita , V. Shcherbakov

Consider a system of interacting particles indexed by the nodes of a graph whose vertices are equipped with marks representing parameters of the model such as the environment or initial data. Each particle takes values in a countable state…

Probability · Mathematics 2022-10-18 Ankan Ganguly , Kavita Ramanan

Adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on…

Statistical Mechanics · Physics 2015-06-15 Maxim S. Shkarayev , Leah B. Shaw

It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To…

Applications · Statistics 2017-04-21 Lourens J. Waldorp , Jolanda J. Kossakowski

We study the asymptotic behaviour of Markov processes on large weighted Erdos-Renyi graphs where the transition rates of the vertices are only influenced by the state of their neighbours and the corresponding weight on the edges. We find…

Probability · Mathematics 2020-04-07 Daniel Keliger , Illes Horvath

We study stochastic pairwise interaction network systems whereby a finite population of agents, identified with the nodes of a graph, update their states in response to both individual mutations and pairwise interactions with their…

Systems and Control · Electrical Eng. & Systems 2024-10-31 Giacomo Como , Fabio Fagnani , Sandro Zampieri

The Vlasov-Poisson system for ions is a kinetic equation for dilute, unmagnetised plasma. It describes the evolution of the ions in a plasma under the assumption that the electrons are thermalized. Consequently, the Poisson coupling for the…

Analysis of PDEs · Mathematics 2026-05-15 Megan Griffin-Pickering

We consider the asymptotics of the invariant measure for the process of the empirical spatial distribution of $N$ coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle.…

Probability · Mathematics 2013-01-25 Vivek S. Borkar , Rajesh Sundaresan

We consider interacting agent systems with a large number of stochastic agents (or particles) influenced by a fixed number of external stochastic lead agents. Such examples arise, for example in models of opinion dynamics, where a small…

Optimization and Control · Mathematics 2025-12-23 Sebastian Zimper , Ana Djurdjevac , Carsten Hartmann , Christof Schütte , Nataša Djurdjevac Conrad

Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…

Probability · Mathematics 2024-01-02 Kavita Ramanan