A Schelling model with a variable treshold in a closed city segregation model. Analysis of the universality classes

TL;DR

This paper investigates how sudden and gradual changes in tolerance levels influence urban segregation patterns using a Schelling model with variable thresholds, revealing universality classes and clustering behaviors.

Contribution

It introduces a Schelling model with dynamic tolerance thresholds and analyzes the resulting segregation patterns and boundary properties, linking them to universality classes.

Findings

Gradual tolerance decrease leads to different final states depending on change rate.

Sudden drops in tolerance produce clustered segregation with boundaries in the Edward-Wilkinson universality class.

The model highlights the impact of tolerance dynamics on urban segregation structures.

Abstract

Residential segregation is analyzed via the Schelling model, in which two types of agents attempt to optimize their situation according to certain preferences and tolerance levels. Several variants of this work are focused on urban or social aspects. Whereas these models consider fixed values for wealth or tolerance, here we consider how sudden changes in the tolerance level affect the urban structure in the closed city model. In this framework, when tolerance decreases continuously, the change rate is a key parameter for the final state reached by the system. On the other hand, sudden drops in tolerance tend to group agents into clusters whose boundary can be characterized using tools from kinetic roughening. This frontier can be categorized into the Edward-Wilkinson (EW) universality class. Likewise, the understanding of these processes and how society adapts to tolerance variations are of the utmost importance in a world where migratory movements and pro-segregational attitudes are commonplace.