摘要翻译：
Zipf定律指出，规模大于S的公司数量与S成反比。大多数解释从直布罗特的比例增长规则开始，但需要额外的约束。我们证明，在现有企业（包括其可能的消亡）的有效增长率和进入企业的投资增长率之间的平衡条件下，在所有企业层面上，直布罗特规则都产生了Zipf定律。值得注意的是，齐普夫定律是确保经济最大可持续增长率的资源长期最优配置的标志。
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英文标题：
《Zipf's law and maximum sustainable growth》
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作者：
Y. Malevergne, A. Saichev and D. Sornette
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最新提交年份：
2010
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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：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要：
  Zipf's law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but require additional constraints. We show that Gibrat's rule, at all firm levels, yields Zipf's law under a balance condition between the effective growth rate of incumbent firms (which includes their possible demise) and the growth rate of investments in entrant firms. Remarkably, Zipf's law is the signature of the long-term optimal allocation of resources that ensures the maximum sustainable growth rate of an economy.
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PDF链接：
https://arxiv.org/pdf/1012.0199