Wishart-Levy自由稳定随机矩阵的谱密度：解析结果和Monte Carlo验证
Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validation
摘要：
随机矩阵理论用于评估弱相关性的重要性，并已为高斯统计量建立。然而，许多复杂系统，股票市场作为一个突出的例子，表现出统计与幂律尾部，可以与利维稳定分布建模。本文全面回顾了自由Levy稳定随机变量近似协方差矩阵谱的解析表达式的推导，并通过蒙特卡罗模拟进行了验证。
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
