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摘要翻译：
随机矩阵理论被用来评估弱相关性的重要性，并被很好地建立在高斯统计量上。然而，许多复杂系统，以股票市场为突出例子，表现出具有幂律尾的统计量，可以用Levy稳定分布来建模。本文全面回顾了自由Levy稳定随机变量近似的协方差矩阵谱的解析表达式的推导，并用蒙特卡罗模拟对其进行了验证。
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英文标题：
《Spectral densities of Wishart-Levy free stable random matrices:
Analytical results and Monte Carlo validation》
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作者：
Mauro Politi, Enrico Scalas, Daniel Fulger, and Guido Germano
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最新提交年份：
2009
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with Levy stable distributions. We review comprehensively the derivation of an analytical expression for the spectra of covariance matrices approximated by free Levy stable random variables and validate it by Monte Carlo simulation.
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PDF链接：
https://arxiv.org/pdf/0903.1629
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