Related papers: Partial mean field limits in heterogeneous network…
We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as…
The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…
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…
We study some systems of interacting fields whose evolution is given by some singular stochastic partial differential equations of mean field type. We provide a robust setting for their study and prove a well-posedness result and a…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…
In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…
This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…
Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as $n$ interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or…
A system of interacting multiclass finite-state jump processes is analyzed. The model under consideration consists of a block-structured network with dynamically changing multi-colors nodes. The interaction is local and described through…
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…
This paper deals with the derivation of the mean-field limit for multi-agent systems on a large class of sparse graphs. More specifically, the case of non-exchangeable multi-agent systems consisting of non-identical agents is addressed. The…
Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in these areas are driven by neural networks. There are also…
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…
We study stochastic particle systems made up of heterogeneous units. We introduce a general framework suitable to analytically study this kind of systems and apply it to two particular models of interest in economy and epidemiology. We show…
We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
Several differential equation models have been proposed to explain the formation of patterns characteristic of the grid cell network. Understanding the robustness of these patterns with respect to noise is one of the key open questions in…
This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly…
We study the mean-field limit of a generic class of dynamic co-evolving latent space networks motivated by the social and opinion dynamics literature. Such models include $n$ agents, whose opinions are given by latent stochastic processes,…
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…