摘要翻译：
本文研究了随机变量ω=x_1/(x_1+x_2)的分布P(ω)，x_1和x_2是从同一回火Paretian系综中随机选择的两个个体的财富，其特征为分布\psi(x)\sim\phi(x)/x^{1+\alpha},其中alpha>0是Pareto指数，$phi(x)$是截止函数。我们考虑了\phi(x)的两种形式：对于L\leqx\leqh是有界函数\phi(x)=1，否则为零；对于光滑指数函数\phi(x)=\exp(-L/x-x/H)。在这两种情况下\psi(x)都具有任意阶矩。我们证明，对于α>1，P(\omega)总是一个单峰形式，并且在\omega=1/2处达到顶峰，因此x_1\很可能约为x_2。对于0<\alpha<1，我们观察到一个更复杂的行为，它依赖于\delta=L/H的值。特别地，对于\delta<\delta_c-某个阈值-P(\omega)具有三模态（对于有界\phi(x))和双模态M形（对于指数\phi(x))形式，这表明在这样的系综中，财富x_1和x_2不成比例地不同。
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英文标题：
《Proportionate vs disproportionate distribution of wealth of two
  individuals in a tempered Paretian ensemble》
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作者：
G. Oshanin, Yu. Holovatch and G. Schehr
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最新提交年份：
2011
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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：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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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：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：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  We study the distribution P(\omega) of the random variable \omega = x_1/(x_1 + x_2), where x_1 and x_2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution \Psi(x) \sim \phi(x)/x^{1 + \alpha}, where \alpha > 0 is the Pareto index and $\phi(x)$ is the cut-off function. We consider two forms of \phi(x): a bounded function \phi(x) = 1 for L \leq x \leq H, and zero otherwise, and a smooth exponential function \phi(x) = \exp(-L/x - x/H). In both cases \Psi(x) has moments of arbitrary order.   We show that, for \alpha > 1, P(\omega) always has a unimodal form and is peaked at \omega = 1/2, so that most probably x_1 \approx x_2. For 0 < \alpha < 1 we observe a more complicated behavior which depends on the value of \delta = L/H. In particular, for \delta < \delta_c - a certain threshold value - P(\omega) has a three-modal (for a bounded \phi(x)) and a bimodal M-shape (for an exponential \phi(x)) form which signifies that in such ensembles the wealths x_1 and x_2 are disproportionately different.
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PDF链接：
https://arxiv.org/pdf/1106.4710