Related papers: Partial mean field limits in heterogeneous network…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
A principled method to obtain approximate solutions of general constrained integer optimization problems is introduced. The approach is based on the calculation of a mean field probability distribution for the decision variables which is…
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…
We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…
This paper investigates mean field games and control on sparse networks. In the case of large expander graphs, the limit topologies are analyzed using the graphexon framework, which characterizes both dense network limits and sparse…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
This paper regards randomized discrete-time consensus systems that preserve the average "on average". As a main result, we provide an upper bound on the mean square deviation of the consensus value from the initial average. Then, we apply…
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…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
We use scaling results to identify the crossover to mean-field behavior of equilibrium statistical mechanics models on a variant of the small world network. The results are generalizable to a wide-range of equilibrium systems. Anomalous…
The manner epidemics occurs in a social network depends on various elements, with two of the most influential being the relationships among individuals in the population and the mechanism of transmission. In this paper, we assume that the…
This paper studies a class of partial information linear-quadratic mean-field game problems. A general stochastic large-population system is considered, where the diffusion term of the dynamic of each agent can depend on the state and…
We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…
We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random…
A probabilistic framework is introduced that represents stylized banking networks and aims to predict the size of contagion events. In contrast to previous work on random financial networks, which assumes independent connections between…
We consider the error arising from the approximation of an N-particle dynamics with its description in terms of a one-particle kinetic equation. We estimate the distance between the j-marginal of the system and the factorized state,…
We consider a system of particles experiencing diffusion and mean field interaction, and study its behaviour when the number of particles goes to infinity. We derive non-asymptotic large deviation bounds measuring the concentration of the…
Fokker-Planck equations represent a suitable description of the finite-time behavior for a large class of particle systems as the size of the population tends to infinity. Recently, the theory of graph limits has been introduced in the…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…