The Dynamics of Schelling-Type Segregation Models and a Nonlinear Graph Laplacian Variational Problem

摘要: In this paper we analyze a variant of the famous Schelling segregation model in economics as dynamical system. This exhibits, what appears to be, new clustering mechanism. particular, explain why limiting behavior non-locally determined lattice system exhibits number pronounced geometric characteristics. Part our analysis uses geometrically defined Lyapunov function which show is essentially total Laplacian for associated graph Laplacian. The limit states are minimizers natural nonlinear, nonhomogeneous variational problem Laplacian, can also be interpreted ground state configurations gas whose Hamiltonian coincides with function. Thus use dynamics explicitly solve there no known analytic solution. We prove an isoperimetric characterization global on torus enables us obtain problem. provide plethora local minimizers.