Tipping Points in Schelling Segregation

Thomas Schelling’s spacial proximity model illustrated how racial segregation can emerge, unwanted, from the actions of citizens acting in accordance with their individual local preferences. One of the earliest agent-based models, it is closely related both to the spin-1 models of statistical physics, and to cascading phenomena on networks. Here a 1-dimensional unperturbed variant of the model is studied, which is open in the sense that agents may enter and exit the model. Following the authors’ previous work [1] and that of Brandt, Immorlica, Kamath, and Kleinberg in [4], rigorous asymptotic results are established. This model’s openness allows either race to take over almost everywhere. Tipping points are identified between the regions of takeover and staticity. In a significant generalization of the models considered in [1] and [4], the model’s parameters comprise the initial proportions of the two races, along with independent values of the tolerance for each race.