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Yuan Zhang : Phase transition in a metapopulation version of Schellings model (Nov 1, 2012 4:25 PM)

In 1971, Schelling introduced a model in which individuals move if they have too many neighbors of the opposite type. In this paper we will consider a metapopulation version of the model in which a city is divided into N neighborhoods each of which has L houses. There are ρ NL red indivdiuals and an equal number of blue individuals. Individuals are happy if the fraction of individuals of the opposite type in their neighborhood, is ≤ ρcand move to vacant houses at rates that depend on their state and that of their destination. Our goal is to show that if L is large then as ρ passes through ρc the system goes from a homogeneous state in which all neighborhoods have \approx ρL of each color to a segregated state in which 1/2 of the neighborhoods have ρ1L reds and ρ2L blues and 1/2 with the opposite composition.

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