摘要翻译：
公共债务是定量描述一个国家经济的重要经济变量之一。因为破产是一种风险，即使是像政府这样大的机构（如冰岛），国家债务应严格控制在国家财富方面。此外，在世界上消除赤贫的问题与对赤贫债务国的研究密切相关。我们分析了国家公共债务的时间演变，发现了“趋同”：最初负债较少的国家比最初负债较多的国家增加债务的速度更快。我们还分析了公债与GDP之比R（违约风险的一个代理），并用伽马分布近似了概率密度函数P(R)，该函数可以用来建立可持续债务的阈值。我们还观察到R的“收敛性”：初始R小的国家比初始R大的国家增加R的速度更快。债务与R的比例关系具有实际应用，例如马斯特里赫特条约要求欧洲货币联盟成员保持R<0.6。
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英文标题：
《Scale invariant properties of public debt growth》
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作者：
Alexander M. Petersen, Boris Podobnik, Davor Horvatic, H. Eugene
  Stanley
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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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：Popular Physics        大众物理学
分类描述：Description coming soon
描述即将到来
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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：
  Public debt is one of the important economic variables that quantitatively describes a nation's economy. Because bankruptcy is a risk faced even by institutions as large as governments (e.g. Iceland), national debt should be strictly controlled with respect to national wealth. Also, the problem of eliminating extreme poverty in the world is closely connected to the study of extremely poor debtor nations. We analyze the time evolution of national public debt and find "convergence": initially less-indebted countries increase their debt more quickly than initially more-indebted countries. We also analyze the public debt-to-GDP ratio R, a proxy for default risk, and approximate the probability density function P(R) with a Gamma distribution, which can be used to establish thresholds for sustainable debt. We also observe "convergence" in R: countries with initially small R increase their R more quickly than countries with initially large R. The scaling relationships for debt and R have practical applications, e.g. the Maastricht Treaty requires members of the European Monetary Union to maintain R < 0.6.
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PDF链接：
https://arxiv.org/pdf/1002.2491