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Semi-annual Workshop on Dynamical Systems and Related Topics
March 18-21, 2000
University of Maryland
College Park, MD, USA

Organizers
Brian R. Hunt, Michael Jakobson

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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

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caep-04.