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摘要翻译：
指数分布在多智能体系统框架中普遍存在。通常在统计系统的渐近时间演化中以平衡态出现。人们从非常不同的角度对其进行了解释。在统计物理学中，它是由最大熵原理得到的。在同样的情况下，它也可以不考虑信息论，只需在相空间中的等概率假设下从几何参数导出。此外，基于映射的多主体经济模型，在随机、确定性或混沌相互作用下，都可以导致财富指数分布的渐近显现。最近在分布空间中的迭代框架中提出了一种解决这个问题的替代方法。具体地，给出了$f_{n+1}(x)=\int\int_{u+v>x}{f_n(u)f_n(v)\over u+v}dudv.$的新迭代。发现指数分布是前泛函迭代方程的稳定不动点。从这一观点出发，很容易理解为什么在不同的多主体经济模型中，指数财富分布（或引申为其他类型的分布）是渐近获得的。
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英文标题：
《Exponential wealth distribution: a new approach from functional
iteration theory》
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作者：
Ricardo Lopez-Ruiz, Jose-Luis Lopez, Xavier Calbet
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最新提交年份：
2011
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分类信息：
一级分类：Physics 物理学
二级分类：Adaptation and Self-Organizing Systems 自适应和自组织系统
分类描述：Adaptation, self-organizing systems, statistical physics, fluctuating systems, stochastic processes, interacting particle systems, machine learning
自适应，自组织系统，统计物理，波动系统，随机过程，相互作用粒子系统，机器学习
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一级分类：Quantitative Biology 数量生物学
二级分类：Genomics 基因组学
分类描述：DNA sequencing and assembly; gene and motif finding; RNA editing and alternative splicing; genomic structure and processes (replication, transcription, methylation, etc); mutational processes.
DNA测序与组装；基因和基序的发现；RNA编辑和选择性剪接；基因组结构和过程（复制、转录、甲基化等）；突变过程。
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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：
Exponential distribution is ubiquitous in the framework of multi-agent systems. Usually, it appears as an equilibrium state in the asymptotic time evolution of statistical systems. It has been explained from very different perspectives. In statistical physics, it is obtained from the principle of maximum entropy. In the same context, it can also be derived without any consideration about information theory, only from geometrical arguments under the hypothesis of equiprobability in phase space. Also, several multi-agent economic models based on mappings, with random, deterministic or chaotic interactions, can give rise to the asymptotic appearance of the exponential wealth distribution. An alternative approach to this problem in the framework of iterations in the space of distributions has been recently presented. Concretely, the new iteration given by $ f_{n+1}(x) = \int\int_{u+v>x}{f_n(u)f_n(v)\over u+v} dudv.$. It is found that the exponential distribution is a stable fixed point of the former functional iteration equation. From this point of view, it is easily understood why the exponential wealth distribution (or by extension, other kind of distributions) is asymptotically obtained in different multi-agent economic models.
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PDF链接：
https://arxiv.org/pdf/1103.1501
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