Exponential segregation in a two-dimensional schelling model with tolerant individuals

Abstract

We prove that the two-dimensional Schelling segregation model yields monochromatic regions of size exponential in the area of individuals' neighborhoods, pro- vided 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.