Stochastic models, agent-based models and social simulations

Presentation

 

From the viewpoint of mathematical modelling and scientific analysis, numerous human systems exhibit challenges similar to the ones posed by complex systems in the physical and natural sciences. We therefore develop and study approaches of stochastic modelling and numerical simulations that are geared specifically toward questions in the humanities and social sciences, while being analogous in spirit to approaches developed in the physics of complex systems.

 

We focus in particular on the definition of a formal framework enabling one to derive, analytically or through simulations, phase diagrams describing the behaviour of complex systems of human, social, historical and economical interactions.

We also seek to ascertain a theoretical framework for the use of agent-based models and other types of numerical simulations in scientific prediction and causal inference.

Diffusion dynamics on networks and socio-spatial phenomena such as segregation are also part of the topics that we study, as well as, on a more pure mathematics note, the properties of stochastic processes (Markov chains, random walks, Lévy processes) that appear in our models – specifically questions related to extreme values, first passage times, rare events and stochastic geometry