Related papers: Interacting particle systems as stochastic social …
This thesis uses a quantity that is defined and justified by information theory -- mutual information -- to examine models of condensed matter systems. More precisely, it studies models which are made up out of ferromagnetically interacting…
Financial markets are a typical example of complex systems where interactions between constituents lead to many remarkable features. Here, we show that a pairwise maximum entropy model (or auto-logistic model) is able to describe switches…
The proliferation of social media such as real time microblogging and online reputation systems facilitate real time sensing of social patterns and behavior. In the last decade, sensing and decision making in social networks have witnessed…
Interacting systems are increasingly common. Many examples pervade our everyday lives: automobiles, aircraft, defense systems, telephone switching systems, financial systems, national governments, and so on. Closer to computer science,…
Communities are an important feature of social networks. In fact, it seems that communities are necessary for a social network to be efficient. However, there exist very few formal studies of the actual role of communities in social…
In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a…
A model of interacting random walkers is presented and shown to give rise to patterns consisting in periodic arrangements of fluctuating particle clusters. The model represents biological individuals that die or reproduce at rates depending…
Interacting particle systems play a key role in science and engineering. Access to the governing particle interaction law is fundamental for a complete understanding of such systems. However, the inherent system complexity keeps the…
We study a stochastic model for the coevolution of a process of opinion formation in a population of agents and the network which underlies their interaction. Interaction links can break when agents fail to reach an opinion agreement. The…
We introduce multi-population opinion dynamics models linked to the bounded confidence model, aiming to explore how interactions between individuals contribute to the emergence of consensus, polarization, or fragmentation. Existing models…
We discuss a stochastic particle system consisting of a two-dimensional array of particles living in one space dimension. The stochastic evolution bears a certain similarity to Hammersley's process, and the particle interaction is governed…
This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…
Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the…
We survey some recent developments on the mathematical modeling of opinion dynamics. After an introduction on opinion modeling through interacting multi-agent systems described by partial differential equations of kinetic type, we focus our…
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes,…
We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…
In this work we investigate how future actions are influenced by the previous ones, in the specific contexts of scientific collaborations and friendships on social networks. We are not interested in modeling the process of link formation…
Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological,…
We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…
We consider a general interacting particle system with interactions on a random graph, and study the large population limit of this system. When the sequence of underlying graphs converges to a graphon, we show convergence of the…