摘要翻译：
已知规模与企业增长率方差之间的关系遵循近似幂律行为$\sigma(S)\sim S^{-\beta(S)}$，其中$S$是企业规模，$\beta(S)\\0.2$是一个弱依赖于$S$的指数。在这里，我们展示了一个比例增长模型如何解释这种规模-方差依赖关系，该模型将企业视为由不同数量的可变规模单位组成的类。通常，该模型预测$\beta(S)$必须表现出从$\beta(0)=0$到$\beta(\infty)=1/2$的交叉。对于一组实际的参数，$\beta(S)$近似为常数，根据公司的平均单位数，可以在0.14到0.2之间变化。我们用一个独特的行业数据库来检验这个模型，在这个数据库中，公司的销售额是用他们所有产品的销售额之和来给出的。我们发现该模型与经验观察到的大小-方差关系是一致的。
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英文标题：
《The Size Variance Relationship of Business Firm Growth Rates》
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作者：
Massimo Riccaboni, Fabio Pammolli, Sergey V. Buldyrev, Linda Ponta and
  H. Eugene Stanley
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最新提交年份：
2009
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分类信息：

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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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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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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英文摘要：
  The relationship between the size and the variance of firm growth rates is known to follow an approximate power-law behavior $\sigma(S) \sim S^{-\beta(S)}$ where $S$ is the firm size and $\beta(S)\approx 0.2$ is an exponent weakly dependent on $S$. Here we show how a model of proportional growth which treats firms as classes composed of various number of units of variable size, can explain this size-variance dependence. In general, the model predicts that $\beta(S)$ must exhibit a crossover from $\beta(0)=0$ to $\beta(\infty)=1/2$. For a realistic set of parameters, $\beta(S)$ is approximately constant and can vary in the range from 0.14 to 0.2 depending on the average number of units in the firm. We test the model with a unique industry specific database in which firm sales are given in terms of the sum of the sales of all their products. We find that the model is consistent with the empirically observed size-variance relationship.
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PDF链接：
https://arxiv.org/pdf/0904.1404