Clustering and Mixing Times for Segregation Models on ℤ2
Clustering and Mixing Times for Segregation Models on ℤ2
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ℤ2 上分离模型的聚类和混合时间
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Dana Randall
中科院分区：
文献类型：
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作者：
Prateek Bhakta;S. Miracle;Dana Randall
谢林隔离模型试图解释城市种族隔离的可能原因。谢林考虑了两种类型的居民，每个人都希望他或她的大多数邻居是同一类型的。他通过模拟表明，如果居民在对当地环境不满意时搬家，即使是这种类型的温和偏好也会导致种族隔离。我们推广谢林模型，包括一个广泛的类别的偏置函数决定个人的幸福或移动的愿望，称为一般影响模型。我们表明，对于该类中的任何影响函数，动态将迅速混合，城市将被整合（即，如果种族偏见足够低，就不会有聚类）。接下来，我们展示了两大类影响函数的互补结果：增加偏置函数（IBF），每次相同颜色的人离开时，个体移动的可能性都会增加（这不包括谢林的阈值模型），阈值偏置函数（TBF）的阈值超过一半，让人想起谢林最初提出的模型。对于这两个类（IBF和TBF），我们表明，当偏见是足够高的，动态需要指数时间来混合，我们将有隔离和一个大的“贫民窟”将形成。
The Schelling segregation model attempts to explain possible causes of racial segregation in cities. Schelling considered residents of two types, where everyone prefers that the majority of his or her neighbors are of the same type. He showed through simulations that even mild preferences of this type can lead to segregation if residents move whenever they are not happy with their local environments. We generalize the Schelling model to include a broad class of bias functions determining individuals happiness or desire to move, called the General Influence Model. We show that for any influence function in this class, the dynamics will be rapidly mixing and cities will be integrated (i.e., there will not be clustering) if the racial bias is sufficiently low. Next we show complementary results for two broad classes of influence functions: Increasing Bias Functions (IBF), where an individual's likelihood of moving increases each time someone of the same color leaves (this does not include Schelling's threshold models), and Threshold Bias Functions (TBF) with the threshold exceeding one half, reminiscent of the model Schelling originally proposed. For both classes (IBF and TBF), we show that when the bias is sufficiently high, the dynamics take exponential time to mix and we will have segregation and a large "ghetto" will form.