摘要翻译：
我们讨论了乘性随机过程在模拟幂律城市规模分布发生过程中的作用。作为对Zipf秩分析结果的解释，Simon模型以数学初等的方式提出，并对所涉及的假设进行了深入的讨论。强调了该模型的灵活性，即它可能的扩展和一些强假设的松弛。我们指出了关于Zipf秩图详细形状预测的一些公开问题，这些问题可以通过这种扩展来解决。
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英文标题：
《Zipf's law and city sizes: A short tutorial review on multiplicative
  processes in urban growth》
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作者：
Damian H. Zanette
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最新提交年份：
2007
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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：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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英文摘要：
  We address the role of multiplicative stochastic processes in modeling the occurrence of power-law city size distributions. As an explanation of the result of Zipf's rank analysis, Simon's model is presented in a mathematically elementary way, with a thorough discussion of the involved hypotheses. Emphasis is put on the flexibility of the model, as to its possible extensions and the relaxation of some strong assumptions. We point out some open problems regarding the prediction of the detailed shape of Zipf's rank plots, which may be tackled by means of such extensions.
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PDF链接：
https://arxiv.org/pdf/704.317