The Dynamics of Schelling-Type Segregation Models and a Graph Laplacian Variational Problem
by
Howard Weiss
Penn State University

We analyze a variant of Schelling segregation model as a dynamical system. In particular, we explain why the limiting behavior of the lattice system exhibits a number of pronounced geometric characteristics.

Part of our analysis uses a geometrically defined Lyapunov function which we show is essentially the total Laplacian for the associated graph Laplacian. The limit states are minimizers of a non-linear, non-homogeneous variational problem for the Laplacian. We prove a grid domain isoperimetric inequality on the torus which allows us to obtain the global minimizers, as well as to explicitly solve the graph variational problem.

Date received: March 4, 2000