We derived the critical neighborhood demand in the Schelling's segregationmodel by studying the conditions for which a chain reaction of migrations ofunsatisfied agents occurs. The essence of Schelling dynamics was approximatedin two simplified models: (1) a random walk model for the initial stage of themigrations to illustrate the power-law behavior of chain reaction lengths undercritical conditions, and (2) a two-room model for the whole process torepresent a non-spatial version of segregation dynamics in the Schelling model.Our theoretical results showed good agreements with numerical results obtainedfrom agent-based simulations.
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