Zipf's and Taylor's laws
Zipf's and Taylor's laws
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DOI：
10.1103/physreve.98.032408
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发表时间：
2018-09-12
影响因子：
2.4
通讯作者：
Simini, Filippo
中科院分区：
文献类型：
--
作者：
James, Charlotte;Azaele, Sandro;Simini, Filippo
齐普夫定律指出，具有给定值的观测频率与该值的平方成反比；相反，泰勒定律描述的是人口规模波动与其平均值之间的比例关系。这些定律有效性的经验证据已经在许多不同的领域找到。尽管提出了许多模型来解释齐普夫定律的存在，但对于它如何起源于没有微调的个体动力学的微观过程，还没有达成共识。在这里，我们证明了Zipf定律和Taylor定律可以出现在个体水平上的一类一般随机过程中，这些随机过程包含两个特征之一：环境变异性，即参数的波动，或相关性，即个体之间的相关性。在这些假设下，我们用数值方法和理论论证证明了总体增量的条件方差随总体的平方而变化，相应的平稳分布服从Zipf定律。
Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean. Empirical evidence of the validity of these laws has been found in many and diverse domains. Despite the numerous models proposed to explain the presence of Zipf's law, there is no consensus on how it originates from a microscopic process of individual dynamics without fine-tuning. Here we show that Zipf's law and Taylor's law can emerge from a general class of stochastic processes at the individual level, which incorporate one of two features: environmental variability, i.e., fluctuations of parameters, or correlations, i.e., dependence between individuals. Under these assumptions, we show numerically and with theoretical arguments that the conditional variance of the population increments scales as the square of the population, and that the corresponding stationary distribution of the processes follows Zipf's law.