The Schelling model of segregation looks to explain the way in which apopulation of agents or particles of two types may come to organise itself intolarge homogeneous clusters, and can be seen as a variant of the Ising model inwhich the system is subjected to rapid cooling. While the model has been veryextensively studied, the unperturbed (noiseless) version has largely resistedrigorous analysis, with most results in the literature pertaining to versionsof the model in which noise is introduced into the dynamics so as to make itamenable to standard techniques from statistical mechanics or stochasticevolutionary game theory. We rigorously analyse the one-dimensional version ofthe model in which one of the two types is in the minority, and establishvarious forms of threshold behaviour. Our results are in sharp contrast withthe case when the distribution of the two types is uniform (i.e. each agent hasequal chance of being of each type in the initial configuration), which wasstudied by Brandt, Immorlica, Kamath, and Kleinberg.
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