Hydrodynamic limit of the Schelling model with spontaneous Glauber and Kawasaki dynamics - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Electronic Journal of Probability Année : 2024

Hydrodynamic limit of the Schelling model with spontaneous Glauber and Kawasaki dynamics

Résumé

In the present article we consider the Schelling 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 Schelling model was analyzed along several directions, notably by exploiting theoretical physics tools and computer simulations. This approach led to conjecture a phase diagram in which either different social groups were segregated in two large clusters or they were mixed. As far as the authors know, a rigorous mathematical analysis of some aspect of the model has been made by Holden and Sheffield. In this article, we describe and analyze a perturbation of the the Schelling model as a particle system model by adding a Glauber and Kawasaki dynamics to the original Schelling dynamics. We prove the existence of an hydrodynamic limit described by a reaction-diffusion 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, as in other variations of this model, the existence of a phase diagram in which we have a mixed, a segregated and a metastable segregation phase.
Fichier principal
Vignette du fichier
2302.09866.pdf (929.87 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03996809 , version 1 (20-02-2023)
hal-03996809 , version 2 (20-03-2023)
hal-03996809 , version 3 (14-02-2024)

Identifiants

Citer

Florent Barret, Torri Niccolo. Hydrodynamic limit of the Schelling model with spontaneous Glauber and Kawasaki dynamics. Electronic Journal of Probability, 2024, 29 (none), ⟨10.1214/24-EJP1078⟩. ⟨hal-03996809v3⟩
42 Consultations
16 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More