摘要翻译:
许多不同的物理和社会经济系统的秩-大小图通常被认为遵循Zipf定律,但仍然缺乏一个独特的框架来理解这个普遍存在的标度定律。在这里,我们表明一个动力学的方法是至关重要的:在它们的演化过程中,一些系统被Zipf定律所吸引,而另一些系统只是暂时地呈现Zipf定律,因此,是虚假的。一个真正的Zipfian动力学的特征是在生成PDF的参数和系统中元素的数量之间存在动力学约束或一致性。这种连贯性的一个明显例子是自然语言。我们的框架允许我们得到一些远远超出通常齐普夫定律的定量结果:i)地震只能不相干地演化,从而虚假地显示齐普夫定律;这使得可以评估发生在一个地理区域的地震的最大可能的震级。(ii)我们证明了Zipfian动力学不是加性的,并分析解释了为什么美国城市发展是一致的,而世界城市却不是一致的;(iii)我们的一致性概念可以用于模型选择,例如,Yule-Simon过程可以描述世界各国GDP的动态变化;(iv)世界城市呈现虚假的Zipf定律,我们用这个性质来估计一个城市群的最大人口。
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英文标题:
《Dynamical approach to Zipf's law》
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作者:
Giordano De Marzo, Andrea Gabrielli, Andrea Zaccaria, and Luciano
Pietronero
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最新提交年份:
2020
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分类信息:
一级分类:Physics 物理学
二级分类:Physics and Society 物理学与社会
分类描述:Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体(人类或其他)的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统(如能源网、运输网络)的物理和工程。
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一级分类:Economics 经济学
二级分类:General Economics 一般经济学
分类描述:General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类:Quantitative Finance 数量金融学
二级分类:Economics 经济学
分类描述:q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学,包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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英文摘要:
The rank-size plots of a large number of different physical and socio-economic systems are usually said to follow Zipf's law, but a unique framework for the comprehension of this ubiquitous scaling law is still lacking. Here we show that a dynamical approach is crucial: during their evolution, some systems are attracted towards Zipf's law, while others presents Zipf's law only temporarily and, therefore, spuriously. A truly Zipfian dynamics is characterized by a dynamical constraint, or coherence, among the parameters of the generating PDF, and the number of elements in the system. A clear-cut example of such coherence is natural language. Our framework allows us to derive some quantitative results that go well beyond the usual Zipf's law: i) earthquakes can evolve only incoherently and thus show Zipf's law spuriously; this allows an assessment of the largest possible magnitude of an earthquake occurring in a geographical region. ii) We prove that Zipfian dynamics are not additive, explaining analytically why US cities evolve coherently, while world cities do not. iii) Our concept of coherence can be used for model selection, for example, the Yule-Simon process can describe the dynamics of world countries' GDP. iv) World cities present spurious Zipf's law and we use this property for estimating the maximal population of an urban agglomeration.
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PDF链接:
https://arxiv.org/pdf/1911.04844