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