Hydrodynamic limit of the Schelling model with spontaneous Glauber and Kawasaki dynamics
Résumé
In the present article we consider the Shelling model, an agent-based model describing a segregation dynamics when we have a cohabitation of two social groups. As for several social models, the behavior of the Shelling model was analyzed by exploiting theoretical physics tools and computer simulations. This approach led to conjecture a phase diagram in which either dierent social groups were segregated in two large clusters or they were mixed. As far as the authors know, this model has never been consider by the mathematical community, a rigorous mathematical analysis of the model is one of the main novelties of the paper. We describe the Shelling model as a particle system model and, adding a Glauber and Kawasaki dynamics to the original Schelling dynamics, we prove the existence of an hydrodynamic limit described by a reaction-diusion equation with a discontinuous non-linear reaction term. The existence and uniqueness of the solution is non trivial and the analysis of the limit PDE is interesting in its own. Based on our results, we conjecture the existence of a phase diagram in which we have a mixed, a segregated and a metastable segregation phase.
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY - Paternité
Licence : CC BY - Paternité