Exponential Segregation in a Two-Dimensional Schelling Model with Tolerant Individuals

TL;DR

This paper proves that in a two-dimensional Schelling segregation model with tolerant individuals, large monochromatic regions form exponentially in size, using a connection to first-passage percolation theory.

Contribution

It establishes a rigorous proof of exponential growth of segregated regions in the Schelling model near the tolerance threshold, linking it to stochastic process theory.

Findings

Monochromatic regions grow exponentially with neighborhood area.

Segregation occurs even with high tolerance levels close to 1/2.

The analysis connects segregation dynamics to first-passage percolation.

Abstract

We prove that the two-dimensional Schelling segregation model yields monochromatic regions of size exponential in the area of individuals' neighborhoods, provided that the tolerance parameter is a constant strictly less than 1/2 but sufficiently close to it. Our analysis makes use of a connection with the first-passage percolation model from the theory of stochastic processes.