Aging effects in Schelling Segregation model

TL;DR

This paper introduces an aging mechanism into the Schelling segregation model, revealing that aging alters phase transitions, promotes high satisfaction in segregation, and results in slow, glassy dynamics in the system.

Contribution

It presents a novel aging extension to the Schelling model, showing significant impacts on phase behavior and dynamic properties not observed in the original model.

Findings

Aging removes the phase transition between segregated and mixed states.

High satisfaction levels persist in segregated states even at high tolerance.

The model exhibits slow power-law coarsening and glassy dynamics.

Abstract

The Schelling model has become a paradigm in social sciences to explain the emerge of residential spatial segregation even in the presence of high tolerance to mixed neighborhoods by the side of citizens. In particular, we consider a noisy constrained version of the Schelling model, in which agents maximize its satisfaction, related to the composition of the local neighborhood, by infinite-range movements towards satisfying vacancies. We add to it an aging effect by making the probability of agents to move inversely proportional to the time they have been satisfied in their present location. This mechanism simulates the development of an emotional attachment to a location where an agent has been satisfied for a while. The introduction of aging has several major impacts on the model statics and dynamics: the phase transition between a segregated and a mixed phase of the original model disappears, and we observe segregated states with high level of agent satisfaction even for high values of the tolerance. In addition, the new segregated phase is dynamically characterized by a slow power-law coarsening process and by a glassy-like dynamics in which the asymptotic time translational invariance is broken.