The dynamics of Schelling-type segregation models and a nonlinear graph Laplacian variational problem. (English) Zbl 0996.91082

This paper concerns a variant of Schelling’s segregation model in economics as a dynamical system. One provides a mathematical explanation for the limiting behaviour. A geometrically defined Lyapunov function, which is essentially the total Laplacian for the associated graph Laplacian, is used. The limit states are minimizers of a nonlinear nonhomogeneous variational problem for the Laplacian. An isoperimetric characterization of the global minimizers on the torus is proved.


91B62 Economic growth models
91B60 Trade models
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