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Minority population in the one-dimensional Schelling model of segregation

机译:一维谢林模型中的少数民族人口   隔离

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摘要

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.
机译:Schelling的分离模型旨在解释两种类型的媒介物或颗粒的聚集可能如何将其自身组织成较大的均匀簇,并且可以看作是Ising模型的变体,在该模型中,系统进行了快速冷却。尽管对该模型进行了广泛的研究,但无干扰(无噪声)版本在很大程度上拒绝了严格的分析,文献中的大多数结果都与该模型的版本有关,在该版本中,将噪声引入了动力学,从而使统计技术或统计技术可以理解为标准技术。随机进化博弈论。我们严格分析模型的一维版本,其中两种类型中的一种处于少数,并建立阈值行为的各种形式。我们的结果与两种类型的分布是均匀的情况形成鲜明对比(即,每种药物在初始构型中都有相同的机会成为每种类型),这是由Brandt,Immorlica,Kamath和Kleinberg研究的。

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